DECIMAL, BINARY, AND HEXADECIMAL
DECIMAL, BINARY, AND
HEXADECIMAL
Decimal Numbering System
Ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Represent larger numbers as a sequence of digits
? Each digit is one of the available symbols
Example: 7061 in decimal (base 10)
? 706110 = (7 x 103) + (0 x 102) + (6 x 101) + (1 x 100)
Octal Numbering System
Eight symbols: : 0, 1, 2, 3, 4, 5, 6, 7
? Notice that we no longer use 8 or 9
Base Comparison:
Base 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12¡
Base 8: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14¡
Example: What is 158 in base 10?
? 158 = (1 x 81) + (5 x 80) = 1310
Example: What is 70618 in base 10?
? 70618 = (7 x 83) + (0 x 82) + (6 x 81) + (1 x 80) = 363310
Question
What is 348 in base 10?
(A)
(B)
(C)
(D)
(E)
3210
3410
710
2810
3510
Binary Numbering System
Binary is base 2
? Symbols: 0, 1
Convention: 210 = 102 = 0b10
Base 10
0
1
2
3
4
5
6
7
8
9
Base 8
0
1
2
3
4
5
6
7
10
11
Example: What is 0b110 in base 10?
? 0b110 = 1102
= (1 x 22) + (1 x 21) + (0 x 10) = 610
Base 2
0
1
10
11
100
101
110
111
1000
1001
................
................
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