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Example 4: Convert the decimal number Example 5: Convert the decimal number (125)
10
(50) to binary. to binary.
10
2 125
2 50 2 62 – 1
2 25 – 0 2 31 – 0
2 12 – 1 2 15 – 1
2 6 – 0 2 7 – 1
2 3 – 0 1 3 – 1
1 – 1
1 – 1
Binary equivalent: 110010 Binary equivalent: 1111101
Example 6: Convert the decimal number Example 7: Convert the decimal number (192)
10
(83) to binary. to binary.
10
2 83 2 192
2 41 – 1 2 96 – 0
2 20 – 1 2 48 – 0
2 10 – 0 2 24 – 0
2 5 – 0 2 12 – 0
2 2 – 1 2 6 – 0
1 – 0 2 3 – 0
1 – 1
Binary equivalent: 1010011 Binary equivalent: 11000000
Binary to Decimal Conversion
To convert a binary number into a decimal number, follow the these steps:
Step 1 Start from the right-most digit known as the LSD before the fractional point, and
move leftwards.
Step 2 While doing so, multiply each digit by 2 raised to a particular power. The powers of 2
start from 0 and increase to 1, 2, and so on as you move leftwards.
Step 3 Add up all the resulting products. You will get your decimal number.
The following examples will help you to understand the conversion.
Example 1: Convert (1111) to decimal. Example 2: Convert (10111) to decimal.
2 2
4
1
2
3
0
3
2
1
= 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2 = 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 × 2 0
= 8 + 4 + 2 + 1 = 16 + 0 + 4 + 2 + 1
= 15 = 23
(1111) = (15) (10111) = (23)
2 10 2 10
Number System 11

