http://proglit.com/. numbers by sa
TRANSCRIPT
![Page 1: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/1.jpg)
http://proglit.com/
![Page 2: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/2.jpg)
numbers
![Page 3: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/3.jpg)
BY
SA
![Page 4: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/4.jpg)
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01bit
(one of two states)
![Page 12: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/12.jpg)
![Page 13: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/13.jpg)
number system(a scheme for symbolically and verbally
representing quantity)
![Page 14: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/14.jpg)
unary(the tally system)
![Page 15: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/15.jpg)
Aiwt$e#&!)9?
![Page 16: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/16.jpg)
positional notation(represents arbitrarily large quantities
using a finite set of symbols)
![Page 17: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/17.jpg)
decimalbase-10
(positional notation using 10 symbols)
![Page 18: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/18.jpg)
Arabic numerals
0 1 2 3 4 5 6 7 8 9
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3940
![Page 20: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/20.jpg)
909
…0000000009
![Page 21: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/21.jpg)
0910
![Page 22: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/22.jpg)
8699987000
![Page 23: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/23.jpg)
78seventy-eightseven eight
![Page 24: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/24.jpg)
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octalbase-8
(positional notation using 8 symbols)
![Page 26: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/26.jpg)
0 1 2 3 4 5 6 7
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0710
![Page 28: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/28.jpg)
12345671011121314
123456789101112
octalbase-8
decimalbase-10
![Page 29: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/29.jpg)
151617202122232425262730
131415161718192021222324
octalbase-8
decimalbase-10
![Page 30: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/30.jpg)
317777320000
![Page 31: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/31.jpg)
61 (decimal)061 (octal)
![Page 32: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/32.jpg)
05673
![Page 33: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/33.jpg)
hexadecimalhex
base-16
(positional notation using 16 symbols)
![Page 34: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/34.jpg)
0 1 2 3 4 5 6 78 9 A B C D E F
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0F10
![Page 36: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/36.jpg)
123456789ABC
123456789101112
hexbase-16
decimalbase-10
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DEF101112131415161718
131415161718192021222324
hexbase-16
decimalbase-10
![Page 38: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/38.jpg)
191A1B1C1D1E1F2021222324
252627282930313233343536
hexbase-16
decimalbase-10
![Page 39: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/39.jpg)
ADDBAD
BEADBEE
BEEF CAFE DEAD DEAF DEED FAD
FEED
![Page 40: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/40.jpg)
0xADD0xBAD
0xBEAD0xBEE
0xBEEF 0xCAFE 0xDEAD 0xDEAF 0xDEED 0xFAD
0xFEED
![Page 41: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/41.jpg)
0xA3BFFFFF0xA3C00000
![Page 42: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/42.jpg)
binarybase-2
(positional notation using 2 symbols)
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0 1
![Page 44: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/44.jpg)
0110
![Page 45: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/45.jpg)
11011
100101110111
10001001101010111100
123456789101112
binarybase-2
decimalbase-10
![Page 46: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/46.jpg)
131415161718192021222324
binarybase-2
decimalbase-10
110111101111100001000110010100111010010101101101011111000
![Page 47: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/47.jpg)
101b (binary)101 (decimal)
![Page 48: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/48.jpg)
10101111b10110000b
![Page 49: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/49.jpg)
http://proglit.com/
![Page 50: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/50.jpg)
base conversions
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36259
![Page 52: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/52.jpg)
(30000) + (6000) + (200) + (50) + (9)
![Page 53: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/53.jpg)
(3 * 10000) + (6 * 1000) + (2 * 100) + (5 * 10)
+ (9 * 1)
![Page 54: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/54.jpg)
(3 * 104) + (6 * 103) + (2 * 102) + (5 * 101) + (9 * 100)
![Page 55: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/55.jpg)
36259104 103 102 101 100
10000 1000 100 10 1
![Page 56: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/56.jpg)
octal to decimal
![Page 57: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/57.jpg)
03675
![Page 58: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/58.jpg)
(03000) + (0600) + (070) + (05)
![Page 59: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/59.jpg)
(03 * 01000) + (06 * 0100) + (07 * 010) + (05 * 01)
![Page 60: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/60.jpg)
(03 * 0103) + (06 * 0102) + (07 * 0101) + (05 * 0100)
![Page 61: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/61.jpg)
(3 * 83) + (6 * 82) + (7 * 81) + (5 * 80)
![Page 62: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/62.jpg)
(3 * 512) + (6 * 64) + (7 * 8) + (5 * 1)
![Page 63: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/63.jpg)
(1636) + (384) + (56) + (5)
![Page 64: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/64.jpg)
03675 =
2081
![Page 65: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/65.jpg)
decimal to octal
![Page 66: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/66.jpg)
36256
![Page 67: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/67.jpg)
(3 * 104) + (6 * 103)+ (2 * 102) + (5 * 101)+ (6 * 100)
![Page 68: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/68.jpg)
(03 * 0124) + (06 * 0123)+ (02 * 0122) + (05 * 0121)+ (06 * 0120)
![Page 69: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/69.jpg)
(03 * 023420) + (06 * 01750)
+ (02 * 0144) + (05 * 012)+ (06 * 01)
![Page 70: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/70.jpg)
(072460) + (013560)+ (0310) + (062)+ (06)
![Page 71: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/71.jpg)
36256=
0106640
![Page 72: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/72.jpg)
hex to decimal
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0x36E59
![Page 74: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/74.jpg)
(0x3 * 164) + (0x6 * 163) + (0xE * 162) + (0x5 * 161) + (0x9 * 160)
![Page 75: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/75.jpg)
(3 * 65536) + (6 * 4096) + (14 * 256) + (5 * 16) + (9 * 1)
![Page 76: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/76.jpg)
(196608) + (24576) + (3584) + (80) + (9)
![Page 77: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/77.jpg)
0x36E59 =
224857
![Page 78: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/78.jpg)
binary to decimal
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10101b
![Page 80: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/80.jpg)
(1 * 24) + (0 * 23) + (1 * 22) + (0 * 21)+ (1 * 20)
![Page 81: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/81.jpg)
(1 * 16) + (0 * 8) + (1 * 4) + (0 * 2)+ (1 * 1)
![Page 82: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/82.jpg)
(16) + (0) + (4) + (0)+ (1)
![Page 83: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/83.jpg)
10101b=21
![Page 84: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/84.jpg)
10101101b
![Page 85: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/85.jpg)
10101101b128 32 8 4 1
![Page 86: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/86.jpg)
(128) + (32) + (8) + (4)+ (1)
![Page 87: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/87.jpg)
10101101b=
173
![Page 88: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/88.jpg)
22 423 824 1625 3226 6427 12828 25629 512210 1024211 2048212 4096213 8192214 16384215 32768216 65536217 131072218 262144219 524288220 1048576
![Page 89: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/89.jpg)
decimal to binary
![Page 90: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/90.jpg)
1) find biggest fitting power of two
2) subtract it out 3) repeat until left with 0
![Page 91: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/91.jpg)
35872
![Page 92: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/92.jpg)
3587232768 (215)
![Page 93: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/93.jpg)
1???????????????b
![Page 94: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/94.jpg)
35872 - 32768=
3104
![Page 95: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/95.jpg)
31042048 (211)
![Page 96: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/96.jpg)
10001???????????b
![Page 97: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/97.jpg)
3104 – 2048=
1056
![Page 98: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/98.jpg)
10561024 (210)
![Page 99: Http://proglit.com/. numbers BY SA](https://reader036.vdocument.in/reader036/viewer/2022081504/551c0466550346b24f8b4dcd/html5/thumbnails/99.jpg)
100011??????????b
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1056 – 1024=32
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3232 (25)
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10001100001?????b
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32 – 32=0
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1000110000100000b
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why use hex and octal?
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octal to binary(and vice versa)
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01234567
000001010011100101110111
octalbase-8
binarybase-2
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03673
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01234567
000001010011100101110111
octalbase-8
binarybase-2
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03673011110111011b
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1101010110b
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001101010110b01526
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hex to binary(and vice versa)
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0123456789ABCDEF
0000000100100011010001010110011110001001101010111100110111101111
hexbase-16
binarybase-2
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0x7E9011111101001b
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1100101101b0x32D
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recapEach digit is a coefficient of the number base raised to an increasing power.
One technique works for all number base conversions.
Shortcut conversions:• decimal to binary (sum powers of 2)• binary to decimal (subtract out powers of 2)• octal and binary (1 octal digit = 3 binary digits)• hex and binary (1 hex digit = 4 binary digits)
Effectively, hex and octal serve as a compacter way of writing binary.
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http://proglit.com/
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meaning relies upon agreement
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integer(whole number)
58780
-87234
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signed integer
unsigned integer
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0, 1, 2, 3, 4, 5…0b, 1b, 10b, 11b, 100b, 101b…
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n bits = 2n values1 bit = 2 values2 bits = 4 values3 bits = 8 values4 bits = 16 values5 bits = 32 values6 bits = 64 values7 bits = 128 values8 bits = 256 values
etc…
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unsigned value range1 bit = 0..12 bits = 0..33 bits = 0..74 bits = 0..155 bits = 0..316 bits = 0..637 bits = 0..1278 bits = 0..255
etc…
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10000011(negative three)
00000011(positive three)
sign bit
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11111100(negative three)
00000011(positive three)
one’s complement
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11111101(negative three)
00000011(positive three)
two’s complement
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00000011(positive three)
11111101(negative three)
two’s complement
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00000101(negative three in excess-8)
00001011(positive three in excess-8)
excess-n
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00100111(negative three in excess-42)
00101101(positive three in excess-42)
excess-n
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sign bit: -127 to +127one’s complement: -127 to +127two’s complement: -128 to +127
8-bit range
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rational numbers2/51/987/1
-61/1738
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radix-point notation(ratio written as an integer component and a
fractional component, separated by a radix point)
3/41/8-7/1138/20
0.750.125-7.06.9
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36.259
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(30) + (6)
+ (0.2) + (0.05)
+ (0.009)
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(3 * 101) + (6 * 100) + (2 * 10-1) + (5 * 10-2) + (9 * 10-3)
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36.259101 100 10-1 10-2 10-3
10 1 1/10 1/100 1/1000
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062.73281 80 8-1 8-2 8-3
8 1 1/8 1/64 1/512
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10.111b21 20 2-1 2-2 2-3
2 1 1/2 1/4 1/8
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finite rational(rational with a fractional component which can be
expressed with a finite number of digits)
3/4-7/1138/201/3
738/61
0.75-7.06.90.33
12.0983606557…
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a ratio with denominator 2a5b is finite in decimal a ratio with denominator 2a is finite in octal a ratio with denominator 2a is finite in hexa ratio with denominator 2a is finite in binary
all ratios which are finite in binary are also finite in decimal some ratios which are finite in decimal are also finite in binary
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rational as two integers3/4
Numerator: 00000011 Denominator: 00000100
-7/13 Numerator: 11111001 Denominator: 00001101
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fixed-point
57/8111.001b
Integer: 00000111 Fraction: 00100000
(the computing equivalentof radix-point notation)
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scientific notationengineering notation 362.354 = 3.62354 * 102
0.00736234 = 7.36234 * 10-3
989777.1 = 9.897771 * 105
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floating-point
21/21010.1b
1.0101b * 23
Significand: 10101000 Exponent: 00000011
(the computing equivalent of scientific notation)
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6.75
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6.75110b + 0.?b
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0.753/4
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3/41/2 + 1/42-1 + 2-2
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6.75=
110.11b
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110.11b=
1.1011b * 22
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1.1011b * 22
Significand: 11011000Exponent: 00000010
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IEEE floating-point(an international standard)
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http://proglit.com/