digital system and binary numbers (1'st update)
DESCRIPTION
Update of previous uploadTRANSCRIPT
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One characteristic of digital systems is their ability to represent and manipulate discrete elements of information.
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Discrete InformationHuruf
Kartu
Power Ranger
Kotak Papan Catur
Jumlah Mahasiswa
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Discrete Information26 Huruf
52 Kartu
6 Power Ranger
64 Kotak Papan Catur
33 Mahasiswa
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Elemen informasi diskrit diwakili di sistem digital oleh sinyal
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arus,
tegangan
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Sinyal diskrit hanya mempunyai dua nilai
(Biner)
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Bit bernilai 0 dan 1
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Discrete elements of information are represented with groups of bits called binary codes
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contoh kode biner
1:
2:
3:
4:
5:
0001
0010
0011
0100
0101
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Kadang
(1000)2 ≠ (1000)10
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tidak mungkin
(1008)2
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tidak mungkin keliru
00F1
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a digital system is a system that manipulates discrete elements of information represented internally in binary form.
Thus
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Diskrit secara alami
Diambil dari proses kontinu (kuantisasi)
Informasi Diskrit
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Diskrit alami
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Kuantisasi
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Kenapa Digital?
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Dapat diprogram
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Satu alat dapat digunakan untuk bermacam keperluan
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Bilangan Biner
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1395
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1395
seribu tiga ratus sembilan puluh lima
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1395
seribu tiga ratus sembilan puluh lima
1000 + 300 + 90 + 5
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1395
seribu tiga ratus sembilan puluh lima
1000 + 300 + 90 + 5
1 x 1000 + 3 x 100 + 9 x 10 + 5
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1395
seribu tiga ratus sembilan puluh lima
1000 + 300 + 90 + 5
1 x 1000 + 3 x 100 + 9 x 10 + 5
1 x 103 + 3 x 102 + 9 x 101 + 5 x 100
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1395
seribu tiga ratus sembilan puluh lima
1000 + 300 + 90 + 5
1 x 1000 + 3 x 100 + 9 x 10 + 5
1 x 103 + 3 x 102 + 9 x 101 + 5 x 100
4 bit
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1 x 103 + 3 x 102 + 9 x 101 + 5 x 100
a3 x 103 + a2 x 102 + a1 x 101 + a0 x 100
basis 10
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basis 10 secara umum
...+103a3 + 102a2 + 101a1 + 100a0 + 10-1a-1 + 10-2a-2 + 10-3a-3 + ...
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secara umum hanya ditulis koefisennya saja
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Biner
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Biner
...+23a3 + 22a2 + 21a1 + 20a0 + 2-1a-1 + 2-2a-2 + 2-3a-3 + ...
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Biner
...+23a3 + 22a2 + 21a1 + 20a0 + 2-1a-1 + 2-2a-2 + 2-3a-3 + ...
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Biner
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Biner
1101
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Biner
1101
1 x 23 + 1 x 22 + 0 x 21 + 1 x 20
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Biner
1101
1 x 23 + 1 x 22 + 0 x 21 + 1 x 20
8 + 4 + 0 + 1 (desimal)
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Biner
1101
1 x 23 + 1 x 22 + 0 x 21 + 1 x 20
8 + 4 + 0 + 1 (desimal)
13 (desimal)
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Biner
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Biner
10.1
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Biner
10.1
1 x 21 + 0 x 20 + 1 x 2-1
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Biner
10.1
1 x 21 + 0 x 20 + 1 x 2-1
2 + 0 + 0.5 (desimal)
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Biner
10.1
1 x 21 + 0 x 20 + 1 x 2-1
2 + 0 + 0.5 (desimal)
2.5 (desimal)
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Basis-r
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Basis-r
...+r3a3 + r2a2 + r1a1 + r0a0 + r-1a-1 + r-2a-2 + r-3a-3 + ...
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Basis-r
...+r3a3 + r2a2 + r1a1 + r0a0 + r-1a-1 + r-2a-2 + r-3a-3 + ...
nilai ai antara 0 dan r-1
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oktal
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oktal
10.1
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oktal
10.1
1 x 81 + 0 x 80 + 1 x 8-1
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oktal
10.1
1 x 81 + 0 x 80 + 1 x 8-1
8 + 0 + 0.125 (desimal)
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oktal
10.1
1 x 81 + 0 x 80 + 1 x 8-1
8 + 0 + 0.125 (desimal)
8.125 (desimal)
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hexadesimal
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hexadesimal
10.1
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hexadesimal
10.1
1 x 161 + 0 x 160 + 1 x 16-1
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hexadesimal
10.1
1 x 161 + 0 x 160 + 1 x 16-1
16 + 0 + 0.125 (desimal)
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hexadesimal
10.1
1 x 161 + 0 x 160 + 1 x 16-1
16 + 0 + 0.125 (desimal)
16.0625 (desimal)
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Biner
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Biner
210 = 1024 = 1K
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Biner
210 = 1024 = 1K
220 = M
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Biner
210 = 1024 = 1K
220 = M
230 = G
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Biner
210 = 1024 = 1K
220 = M
230 = G
240 = T
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Biner
210 = 1024 = 1K
220 = M
230 = G
240 = T
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Aritmatika bilangan berbasis r mengikuti aturan yang sama dengan bilangan desimal
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Biner
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Biner
11 + 0 = 11
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Biner
11 + 0 = 11
1+1 = 10
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Biner
11 + 0 = 11
1+1 = 10
10+11= 101
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Biner
11 + 0 = 11
1+1 = 10
10+11= 101
11+11 = 110
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octal
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octal
1 + 1 = 2
Monday, August 25, 14
![Page 87: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/87.jpg)
octal
1 + 1 = 2
7 + 1 = 10
Monday, August 25, 14
![Page 88: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/88.jpg)
octal
1 + 1 = 2
7 + 1 = 10
17 +11 = 30
Monday, August 25, 14
![Page 89: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/89.jpg)
octal
1 + 1 = 2
7 + 1 = 10
17 +11 = 30
17 + 1 = 20
Monday, August 25, 14
![Page 90: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/90.jpg)
Monday, August 25, 14
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hexadesimal
Monday, August 25, 14
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hexadesimal
9 + 1 = A
Monday, August 25, 14
![Page 93: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/93.jpg)
hexadesimal
9 + 1 = A
9 + 2 = B
Monday, August 25, 14
![Page 94: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/94.jpg)
hexadesimal
9 + 1 = A
9 + 2 = B
F + 2 = 11
Monday, August 25, 14
![Page 95: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/95.jpg)
hexadesimal
9 + 1 = A
9 + 2 = B
F + 2 = 11
FF + 1 = 100
Monday, August 25, 14
![Page 96: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/96.jpg)
Monday, August 25, 14
![Page 97: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/97.jpg)
Biner
Monday, August 25, 14
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Biner
1 - 1 = 0
Monday, August 25, 14
![Page 99: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/99.jpg)
Biner
1 - 1 = 0
10 - 01 = 01
Monday, August 25, 14
![Page 100: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/100.jpg)
Biner
1 - 1 = 0
10 - 01 = 01
1011 - 1001 =0010
Monday, August 25, 14
![Page 101: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/101.jpg)
Monday, August 25, 14
![Page 102: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/102.jpg)
Octal
Monday, August 25, 14
![Page 103: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/103.jpg)
Octal
10 - 1 = 7
Monday, August 25, 14
![Page 104: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/104.jpg)
Octal
10 - 1 = 7
17 - 10 = 7
Monday, August 25, 14
![Page 105: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/105.jpg)
Octal
10 - 1 = 7
17 - 10 = 7
21 - 17 = 2
Monday, August 25, 14
![Page 106: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/106.jpg)
Monday, August 25, 14
![Page 107: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/107.jpg)
Hexadesimal
Monday, August 25, 14
![Page 108: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/108.jpg)
Hexadesimal
10 - 1 = F
Monday, August 25, 14
![Page 109: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/109.jpg)
Hexadesimal
10 - 1 = F
1A - 11 = 9
Monday, August 25, 14
![Page 110: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/110.jpg)
Hexadesimal
10 - 1 = F
1A - 11 = 9
A0 - 1 = 9F
Monday, August 25, 14
![Page 111: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/111.jpg)
Konversi
Monday, August 25, 14
![Page 112: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/112.jpg)
Monday, August 25, 14
![Page 113: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/113.jpg)
Konversi
Monday, August 25, 14
![Page 114: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/114.jpg)
Konversi
(1)2 = (1)8 = (1)16 = (1)5 = 1 (desimal)
Monday, August 25, 14
![Page 115: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/115.jpg)
Konversi
(1)2 = (1)8 = (1)16 = (1)5 = 1 (desimal)
(1 0000)2 = (20)8 = (10)16 = (31)5 = 16 (desimal)
Monday, August 25, 14
![Page 116: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/116.jpg)
Konversi
(1)2 = (1)8 = (1)16 = (1)5 = 1 (desimal)
(1 0000)2 = (20)8 = (10)16 = (31)5 = 16 (desimal)
(0.000110...)2 = 0.05 (desimal)
Monday, August 25, 14
![Page 117: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/117.jpg)
Konversi
(1)2 = (1)8 = (1)16 = (1)5 = 1 (desimal)
(1 0000)2 = (20)8 = (10)16 = (31)5 = 16 (desimal)
(0.000110...)2 = 0.05 (desimal)
(0.001)2 = 0.125 (desimal)
Monday, August 25, 14
![Page 118: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/118.jpg)
Monday, August 25, 14
![Page 119: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/119.jpg)
Desimal ke binary
Monday, August 25, 14
![Page 120: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/120.jpg)
Desimal ke binary102
Monday, August 25, 14
![Page 121: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/121.jpg)
Desimal ke binary102102 bagi dua
Monday, August 25, 14
![Page 122: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/122.jpg)
Desimal ke binary102102 bagi dua51 sisa 0
Monday, August 25, 14
![Page 123: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/123.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 1
Monday, August 25, 14
![Page 124: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/124.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 1
Monday, August 25, 14
![Page 125: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/125.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 0
Monday, August 25, 14
![Page 126: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/126.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
Monday, August 25, 14
![Page 127: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/127.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 1
Monday, August 25, 14
![Page 128: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/128.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
Monday, August 25, 14
![Page 129: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/129.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah
Monday, August 25, 14
![Page 130: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/130.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah1100110
Monday, August 25, 14
![Page 131: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/131.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah1100110jadi
Monday, August 25, 14
![Page 132: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/132.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah1100110jadi (102)10 = (1100110)2
Monday, August 25, 14
![Page 133: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/133.jpg)
Desimal ke binary102102 bagi dua51 sisa 025 sisa 112 sisa 16 sisa 03 sisa 0
1 sisa 10 sisa 1
tulis dari bawah1100110jadi (102)10 = (1100110)2
Monday, August 25, 14
![Page 134: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/134.jpg)
Monday, August 25, 14
![Page 135: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/135.jpg)
Desimal ke octal
Monday, August 25, 14
![Page 136: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/136.jpg)
Desimal ke octal102
Monday, August 25, 14
![Page 137: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/137.jpg)
Desimal ke octal102102 bagi delapan
Monday, August 25, 14
![Page 138: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/138.jpg)
Desimal ke octal102102 bagi delapan12 sisa 6
Monday, August 25, 14
![Page 139: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/139.jpg)
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 4
Monday, August 25, 14
![Page 140: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/140.jpg)
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 40 sisa 1
Monday, August 25, 14
![Page 141: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/141.jpg)
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 40 sisa 1
Monday, August 25, 14
![Page 142: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/142.jpg)
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 40 sisa 1
jadi
Monday, August 25, 14
![Page 143: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/143.jpg)
Desimal ke octal102102 bagi delapan12 sisa 61 sisa 40 sisa 1
jadi
(102)10 = (146)2
Monday, August 25, 14
![Page 144: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/144.jpg)
Monday, August 25, 14
![Page 145: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/145.jpg)
Desimal ke heksadesimal
Monday, August 25, 14
![Page 146: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/146.jpg)
Desimal ke heksadesimal102
Monday, August 25, 14
![Page 147: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/147.jpg)
Desimal ke heksadesimal102102 bagi enambelas
Monday, August 25, 14
![Page 148: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/148.jpg)
Desimal ke heksadesimal102102 bagi enambelas6 sisa 6
Monday, August 25, 14
![Page 149: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/149.jpg)
Desimal ke heksadesimal102102 bagi enambelas6 sisa 60 sisa 6
Monday, August 25, 14
![Page 150: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/150.jpg)
Desimal ke heksadesimal102102 bagi enambelas6 sisa 60 sisa 6jadi
Monday, August 25, 14
![Page 151: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/151.jpg)
Desimal ke heksadesimal102102 bagi enambelas6 sisa 60 sisa 6jadi (102)10 = (6)16
Monday, August 25, 14
![Page 152: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/152.jpg)
Monday, August 25, 14
![Page 153: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/153.jpg)
Pecahan
Monday, August 25, 14
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Pecahan(0.2)10
Monday, August 25, 14
![Page 155: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/155.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 0
Monday, August 25, 14
![Page 156: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/156.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0
Monday, August 25, 14
![Page 157: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/157.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 1
Monday, August 25, 14
![Page 158: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/158.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 1
Monday, August 25, 14
![Page 159: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/159.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0
Monday, August 25, 14
![Page 160: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/160.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0
Monday, August 25, 14
![Page 161: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/161.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 1
Monday, August 25, 14
![Page 162: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/162.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 1
Monday, August 25, 14
![Page 163: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/163.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0
Monday, August 25, 14
![Page 164: Digital system and binary numbers (1'st update)](https://reader038.vdocument.in/reader038/viewer/2022103116/558cf2c8d8b42a827e8b45d1/html5/thumbnails/164.jpg)
Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0.....
Monday, August 25, 14
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Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0.....(0.22)10 = (0.0011001100...)2
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Pecahan(0.2)10
0.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 00.4 x 2 = 0.8 + 0 0.8 x 2 = 0.6 + 10.6 x 2 = 0.2 + 10.2 x 2 = 0.4 + 0.....(0.22)10 = (0.0011001100...)2
Monday, August 25, 14
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Pecahan
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Pecahan(0.25)10
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Pecahan(0.25)10
0.25 x 2 = 0.5 + 0
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Pecahan(0.25)10
0.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
Monday, August 25, 14
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Pecahan(0.25)10
0.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1 .....
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Pecahan(0.25)10
0.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1 .....(0.25)10 = (0.01)2
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Pecahan(0.25)10
0.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1 .....(0.25)10 = (0.01)2
Monday, August 25, 14
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Monday, August 25, 14
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Pecahan
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Pecahan(0.5)10
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Pecahan(0.5)10
0.5 x 2 = 0.0 + 1
Monday, August 25, 14
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Pecahan(0.5)10
0.5 x 2 = 0.0 + 1
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Pecahan(0.5)10
0.5 x 2 = 0.0 + 1
(0.5)10 = (0.1)2
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Pecahan(0.5)10
0.5 x 2 = 0.0 + 1
(0.5)10 = (0.1)2
Monday, August 25, 14
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Monday, August 25, 14
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Pecahan
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Pecahan(0.125)10
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Pecahan(0.125)10
0.125 x 2 = 0.25 + 0
Monday, August 25, 14
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Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 0
Monday, August 25, 14
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Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
Monday, August 25, 14
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Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
Monday, August 25, 14
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Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
(0.5)10 = (0.001)2
Monday, August 25, 14
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Pecahan(0.125)10
0.125 x 2 = 0.25 + 00.25 x 2 = 0.5 + 00.5 x 2 = 0.0 + 1
(0.5)10 = (0.001)2
Monday, August 25, 14
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Monday, August 25, 14
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Monday, August 25, 14
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Monday, August 25, 14
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Oktal dan Heksadesimal
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(111111111111)2
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(111111111111)2
(111 111 111 111)2 = (7 7 7 7)8
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(111111111111)2
(111 111 111 111)2 = (7 7 7 7)8
(1111 1111 1111)2 = (F F F )16
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Monday, August 25, 14
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Bilangan biner sulit untuk digunakan
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Bilangan biner sulit untuk digunakan
Mengunakan digit yang lebih banyak dari desimal
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Monday, August 25, 14
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Bilangan desimal lebih mudah digunakan
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Bilangan desimal lebih mudah digunakan
namun komputer menggunakan biner
Monday, August 25, 14
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Bilangan desimal lebih mudah digunakan
namun komputer menggunakan biner
konversi desimal ke biner rumit
Monday, August 25, 14
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Monday, August 25, 14
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Octal dan Hexadecimal memperkecil digit
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Monday, August 25, 14
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Monday, August 25, 14
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Monday, August 25, 14
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Complements
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Monday, August 25, 14
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‘negatif ’-nya sebuah bilangan
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Monday, August 25, 14
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menyederhanakan pengurangan
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menyederhanakan pengurangan
(dilakukan dengan penjumlahan)
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menyederhanakan pengurangan
(dilakukan dengan penjumlahan)
hemat sirkuit
Monday, August 25, 14
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Monday, August 25, 14
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Komplemen bilangan berbasis-r
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Komplemen bilangan berbasis-r
komplemen r (radix)
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Komplemen bilangan berbasis-r
komplemen r (radix)
komplemen r-1 (diminished radix)
Monday, August 25, 14
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Monday, August 25, 14
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jika sebuah bilangan N dengan basis r memiliki n digit,
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jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki diminished radix komplemen (rn-1)-N
Monday, August 25, 14
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jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki diminished radix komplemen (rn-1)-N
mis 7 desimal akan memiliki diminished radix komplemen (101-1)-7 = 2
Monday, August 25, 14
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jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki diminished radix komplemen (rn-1)-N
mis 7 desimal akan memiliki diminished radix komplemen (101-1)-7 = 2
07 desimal akan memiliki diminished radix komplemen (102-1)-7 = 92
Monday, August 25, 14
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jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki diminished radix komplemen (rn-1)-N
mis 7 desimal akan memiliki diminished radix komplemen (101-1)-7 = 2
07 desimal akan memiliki diminished radix komplemen (102-1)-7 = 92
Monday, August 25, 14
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Monday, August 25, 14
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diminised radix complement tuk binary
Monday, August 25, 14
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diminised radix complement tuk binary
100 -> (23-1)-100
Monday, August 25, 14
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diminised radix complement tuk binary
100 -> (23-1)-100
= (1000-1)-100
Monday, August 25, 14
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diminised radix complement tuk binary
100 -> (23-1)-100
= (1000-1)-100
= (111)-100
Monday, August 25, 14
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diminised radix complement tuk binary
100 -> (23-1)-100
= (1000-1)-100
= (111)-100
= 011
Monday, August 25, 14
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Monday, August 25, 14
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diminised radix complement tuk binary
Monday, August 25, 14
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diminised radix complement tuk binary
111 -> (23-1)-111
Monday, August 25, 14
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diminised radix complement tuk binary
111 -> (23-1)-111
= (1000-1)-111
Monday, August 25, 14
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diminised radix complement tuk binary
111 -> (23-1)-111
= (1000-1)-111
= (111)-111
Monday, August 25, 14
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diminised radix complement tuk binary
111 -> (23-1)-111
= (1000-1)-111
= (111)-111
= 000
Monday, August 25, 14
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Monday, August 25, 14
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diminised radix complement tuk binary
Monday, August 25, 14
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diminised radix complement tuk binary
101 -> (23-1)-101
Monday, August 25, 14
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diminised radix complement tuk binary
101 -> (23-1)-101
= (1000-1)-101
Monday, August 25, 14
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diminised radix complement tuk binary
101 -> (23-1)-101
= (1000-1)-101
= (111)-101
Monday, August 25, 14
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diminised radix complement tuk binary
101 -> (23-1)-101
= (1000-1)-101
= (111)-101
= 010
Monday, August 25, 14
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jika sebuah bilangan N dengan basis r memiliki n digit,
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jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki radix komplemen (rn)-N
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jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki radix komplemen (rn)-N
mis 7 desimal akan memiliki radix komplemen (101)-7 = 3
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jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki radix komplemen (rn)-N
mis 7 desimal akan memiliki radix komplemen (101)-7 = 3
07 desimal akan memiliki radix komplemen (102)-7 = 93
Monday, August 25, 14
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jika sebuah bilangan N dengan basis r memiliki n digit,
maka akan memiliki radix komplemen (rn)-N
mis 7 desimal akan memiliki radix komplemen (101)-7 = 3
07 desimal akan memiliki radix komplemen (102)-7 = 93
Monday, August 25, 14
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radix complement tuk binary
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radix complement tuk binary
100 -> (23)-100
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radix complement tuk binary
100 -> (23)-100
= (1000)-100
Monday, August 25, 14
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radix complement tuk binary
100 -> (23)-100
= (1000)-100
= (1000)-100
Monday, August 25, 14
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radix complement tuk binary
100 -> (23)-100
= (1000)-100
= (1000)-100
= 100
Monday, August 25, 14
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radix complement tuk binary
Monday, August 25, 14
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radix complement tuk binary
111 -> (23)-111
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radix complement tuk binary
111 -> (23)-111
= (1000)-111
Monday, August 25, 14
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radix complement tuk binary
111 -> (23)-111
= (1000)-111
= 001
Monday, August 25, 14
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radix complement tuk binary
Monday, August 25, 14
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radix complement tuk binary
101 -> (23-1)-101
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radix complement tuk binary
101 -> (23-1)-101
= (1000)-101
Monday, August 25, 14
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radix complement tuk binary
101 -> (23-1)-101
= (1000)-101
= 011
Monday, August 25, 14
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Jika memiliki radix point, hilangkan!
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Jika memiliki radix point, hilangkan!
Kembalikan lagi setelah hitungan
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Pengurangan dengan komplemen
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Pengurangan dengan komplemen
(lebih mudah bagi hardware)
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Pengurangan dengan komplemen
(lebih mudah bagi hardware)
(tak ada pinjaman)
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pengurangan bilangan M-N berdigit n berbasis r
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pengurangan bilangan M-N berdigit n berbasis r
tambahkan M dengan radix komplemen dari N
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pengurangan bilangan M-N berdigit n berbasis r
tambahkan M dengan radix komplemen dari N
M + ( rn - N ) = M - N + rn
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jika M≥N maka penjumlahan akan menghasilkan (end carry)
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jika M≥N maka penjumlahan akan menghasilkan (end carry)
buang end carry
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jika M≥N maka penjumlahan akan menghasilkan (end carry)
buang end carry
yang tersisa merupakan hasilnya
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Jika M < N, maka penjumlahan tidak menghasilkan end carry
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Jika M < N, maka penjumlahan tidak menghasilkan end carry
hasilnya merupakan komplemen (N-M)
Monday, August 25, 14
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Jika M < N, maka penjumlahan tidak menghasilkan end carry
hasilnya merupakan komplemen (N-M)
agar ‘enak’ dilihat, ambil komplemen hasil penjumlahan
Monday, August 25, 14
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Jika M < N, maka penjumlahan tidak menghasilkan end carry
hasilnya merupakan komplemen (N-M)
agar ‘enak’ dilihat, ambil komplemen hasil penjumlahan
beri tanda negatif
Monday, August 25, 14
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Selesai
Dan dia hidup bahagia selama-lamanya...Monday, August 25, 14