Conversion of Binary, Octal and Hexadecimal Numbers
Conversion of Binary, Octal and Hexadecimal Numbers
From Binary to Octal
Starting at the binary point and working left, separate the bits into groups of three and replace each group with the corresponding octal digit.
100010112 = 010 001 011 = 2138
From Binary to Hexadecimal
Starting at the binary point and working left, separate the bits into groups of four and replace each group with the corresponding hexadecimal digit.
100010112 = 1000 1011 = 8B16
From Octal to Binary
Replace each octal digit with the corresponding 3-bit binary string.
2138 = 010 001 011 = 100010112
From Hexadecimal to Binary
Replace each hexadecimal digit with the corresponding 4-bit binary string.
8B16 = 1000 1011 = 100010112
Conversion of Decimal Numbers
From Decimal to Binary
2 139 1 LSD
2 69 1
2 34 0
2 17 1
280
240
220
1
MSD
13910 = 100010112
From Binary to Decimal
100010112 = 1?27 + 0?26 + 0?25 + 0?24 + 1?23 + 0?22 + 1?21 + 1?20 = 128 + 8 + 2 + 1
Conversion of Fractions
Starting at the binary point, group the binary digits that lie to the right into groups of three or four.
0.101112 = 0.101 110 = 0.568 0.101112 = 0.1011 1000 = 0.B816
Problems Convert the following
Binary
Octal
Decimal
Hex
10011010
2705
2705
3BC
Binary
Octal
Decimal
Hex
10011010
232
154
9A
10111000101
2705
1477
5C5
101010010001
5221
2705
A91
1110111100
1674
956
3BC
8 2705 1 8 338 2
16 2705 1 16 169 9
8 42 2
10=A
5
Add
1111 + 1 0 0 1 11000
Subtract
11000
-
1 1 1 1
1001
Multiply
normally
1 1 1 0 = 14 * 1 1 0 1 = 13
1110 0000 1110 + 1 1 1 0 10110110
10011 + 1110 100001
10011
-
1 1 1 1
100
for implementation - add the shifted multiplicands one at a time.
1110 * 1 1 0 1
1110 + 0 0 0 0
01110 + 1 1 1 0 1000110 + 1 1 1 0 1 0 1 1 0 1 1 0 (8 bits)
Divide
1 1 0 1 1111) 11000101|
1111 | 1001101|
1111 | 10001| 0000 | 10001| 1 1 1 1 | 10
1 0 0 1 1101) 1111001|
1101 | 10001|
0000 | 10001| 0000 | 10001| 1 1 0 1 | 100
1 1 0 1101) 1011001|
1101 | 100101|
1101 | 1011| 0 0 0 0 | 1011
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