To Convert From Decimal
Decimal to Binary
Convert 48 to Binary
1. Consider values for each of the columns of binary system
2
8
2
7
256 125
2
6
64
2
5
32
2
4
16
2
3
8
2
2
4
2
1
2
1
1
2. Look for the value in a column that is the nearest but less than the figure you are converting
3. Put a 1 in that column and subtract the value of the column from your original figure so:
2
8
2
7
2
6
2
5
2
4
2
3
2
2
2
1
1
256 125 64 32
1
16 8 4 2 1
48 –32 = 16 so now you have to convert 16 to binary
2. Look for the value in a column that is the nearest but less than the figure you are converting
3. Put a 1 in that column and subtract the value of the column from your original figure so:
2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 1
2 1 256 125 64 32
1
16
1
8 4
16 – 16= 0 you cannot have blank columns so the value in each to the right must be 0
2 8 2 7 2 6 2 5 2 4 2 3 2 2
256 125 64 32
1
16
1
8
0
4
0
2 1
2
0
1
1
0
48 converted to binary is 110000
Try converting 59 to Binary
2
8
2
7
2
6
2
5
2
4
16
1
59 - 32 = 27
27 – 16= 11
11- 8 = 3
256 125 64 32
1
4 is more than 3 so enter a zero in the 4 column
3 – 2 = 1
1 – 1 =0 therefore 59 converted to binary is 111011
The same principle works for other conversions
2
3
8
1
2
2
4
0
2
1
2
1
1
1
1

Decimal to Octal
Convert 8905
8
5
32768
8
4
4096
8
3
512
32768 - 262143 4096 -32767 512 -4095
2 1
8905 –(2 x 4096) = 8905 – 8192 = 713
713 – 512 = 201
201 – (64 x 3) = 201 – 192 = 9
9 - 8 =1
1 - 1 =0 therefore 8905 converts to 21311
8
8
2
64
64 - 511
3
8
1
8
8-63
1
Decimal to Hexadecimal
Remember Hex uses more digits 1,2,3,4,5,6,7,8,9,A,B,C,D,E,F Where A to F represent the decimal equivalent of 10 to 15.
Convert 2857 to hexadecimal
16
3
4096
16
2
256
16
1
16
1
1
2857 – (B x 256 = 2816) = 41
41 – (2 x 16 =32) = 9
9 – 9 = 0
B 2 9
1
1
1-7
1