wooseokkim wkim3@albanywooseok/201fall/slide/lab3.pdf•decimal numeral system (base-10) •binary...
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Number Systems
• Decimal Numeral System (Base-10)• Binary Numeral System (Base-2) • Octal Numeral System (Base-8)• Hexadecimal Numeral System (Base-16)
Number Systems
• Decimal Numeral System • Binary Numeral System – Uses only 0 and 1 digits• Octal Numeral System – Uses from 0 ~ 7 digits• Hexadecimal Numeral System – Uses from 0 ~ 9 and A ~ F
Decimal Binary Octal Hexadecimal
0 0000 0 0
1 0001 1 1
2 0010 2 2
3 0011 3 3
4 0100 4 4
5 0101 5 5
6 0110 6 6
7 0111 7 7
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
Convert Decimal to Binary
532
262
132
62
32
12
remainder = 1 = a0
remainder = 0 = a1
remainder = 1 = a2
remainder = 0 = a3
remainder = 1 = a4
0 remainder = 1 = a5
Read
Convert Binary to Decimal
111001
111001 1 2 1 2 1 2 0 2 0 2 1 232 16 8 0 0 1 = 57
Binary Number
1 1 1 0 0 1
Power of 2 2 2 2 2 2 2
Convert Decimal to Hexadecimal
3536116
222616
13916
816
0
remainder = 15 = F = a0
remainder = 2 = a1
remainder = 11 = B = a2
remainder = 8 = a3
Read
Convert Hexadecimal to Decimal
• 3
• 3 3 16 16 48 11 1 59
HEX 3 B
Power of 16 16 16
Convert Binary to Hexadecimal
• Convert each hexadecimal digit into 4 bits binary• : Make bits’ groups
1654
2 5.41100 0101 1101 0100010111.1001101 CDCD
Hexadecimal to BinaryHEX BIN
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
A 1010
B 1011
C 1100
D 1101
E 1110
F 1111
=
SummaryPositional notation
Decimal
Binary
Radix
Octal
Hexadecimal
33
22
11
00
11
22
33
44
32101234
).(
RaRaRa
RaRaRaRaRa
aaaaaaaaN R
10
10128
375.1038373264838784813.147
2101210 10810710310510978.953
10
2101232
75.114311
41
211208
21212121202111.1011
10012
16 260715322560161516216102 FA
Summary
35361R
XXXXR
XXXR
XR
0
remainder = a0
remainder = a1
remainder = a2
remainder = a3
Read
ASCII Table
• American Standard Code for Information Interchange
• Character Encoding Standard
ASCII Table