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
2 69
1
1
2
34
0
2
17
1
2
8
0
2
4
0
2
2
0
1
LSD
13910 = 100010112
MSD
From Binary to Decimal
100010112
= 1¡Á27 + 0¡Á26 + 0¡Á25 + 0¡Á24 + 1¡Á23 + 0¡Á22 + 1¡Á21 + 1¡Á20
= 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
10011010
Octal
Decimal
Hex
2705
2705
3BC
Binary
10011010
10111000101
101010010001
1110111100
Octal
232
2705
5221
1674
8 2705 1
8 338 2
8
42 2
5
Decimal
154
1477
2705
956
16 2705 1
16 169 9
10=A
Hex
9A
5C5
A91
3BC
Add
1
1
1
1
+ 1
0
0
1
+
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
Subtract
1
-
-
Multiply
normally
for implementation - add the shifted
multiplicands one at a time.
1
1
1
0
= 14
1
1
0
1
= 13
1
1
1
0
0
0
0
0
1
1
1
0
+ 1
1
1
0
1
1
1
0
*
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
+ 0
0
0
0
0
1
1
1
0
+ 1
1
1
0
1
0
0
0
1
1
0
+ 1
1
1
0
1
1
1
0
1
1
0
*
0
0
(8 bits)
Divide
1101
110
1111) 11000101|
1111
|
1001101|
1111
|
1101) 1011001|
1101
|
100101|
1101
|
10001|
1011|
0000
0000|
|
10001|
1111|
10
1001
1101) 1111001|
1101
|
10001|
0000
|
10001|
0000
|
10001|
1101|
100
1011
................
................
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