# Binary fractions to decimal numbers

This post is explain

Example 1:

Convert binary number 0.1101 to decimal number

Completion:

0.101

1st digit after binary point: 1 → 1 × (1/ 2

2nd digit after binary point: 0 → 0 × (1/ 2

3rd digit after binary point: 1 → 1 × (1/ 2

sum all → 0.5 + 0 + 0.125 = 0.625

0.101

Example 2:

Convert binary number 1110.11011 to decimal number

Completion:

1110.11011

1st digit: 0 → 1 × 2

2nd digit: 1 → 1 × 2

3rd digit: 1 → 1 × 2

4th digit: 1 → 1 × 2

sum all → 0 + 2 + 4 + 8 = 14

1st digit: 1 → 1 × (1/ 2

2nd digit: 1 → 1 × (1/ 2

3rd digit: 0 → 0 × (1/ 2

4th digit: 1 → 1 × (1/ 2

5th digit: 1 → 1 × (1/ 2

sum all → 0.5 + 0.25 + 0 + 0.0625 + 0.03125 = 0.84375

1110.11011

**how to convert binary fractions to decimal numbers**. The picture below is show binary fraction to decimal, form 1st position to 5th position of the digit, before and after the binary point.Binary fractions to decimal |

Convert binary number 0.1101 to decimal number

Completion:

0.101

_{(2)}= ...

_{(10)}

1st digit after binary point: 1 → 1 × (1/ 2

^{1}) = 1 × 0.5 = 0.5

2nd digit after binary point: 0 → 0 × (1/ 2

^{2}) = 0 × 0.25 = 0

3rd digit after binary point: 1 → 1 × (1/ 2

^{3}) = 1 × 0.125 = 0.125

sum all → 0.5 + 0 + 0.125 = 0.625

0.101

_{(2)}= 0.625

_{(10)}

Example 2:

Convert binary number 1110.11011 to decimal number

Completion:

1110.11011

_{(2)}= ...

_{(10)}

*before binary point*

1st digit: 0 → 1 × 2

^{0}= 0 × 1 = 0

2nd digit: 1 → 1 × 2

^{1}= 1 × 2 = 2

3rd digit: 1 → 1 × 2

^{2}= 1 × 4 = 4

4th digit: 1 → 1 × 2

^{3}= 1 × 8 = 8

sum all → 0 + 2 + 4 + 8 = 14

*after binary point*

1st digit: 1 → 1 × (1/ 2

^{1}) = 1 × 0.5 = 0.5

2nd digit: 1 → 1 × (1/ 2

^{2}) = 1 × 0.25 = 0.25

3rd digit: 0 → 0 × (1/ 2

^{3}) = 0 × 0.125 = 0

4th digit: 1 → 1 × (1/ 2

^{4}) = 1 × 0.0625 = 0.0625

5th digit: 1 → 1 × (1/ 2

^{5}) = 1 × 0.03125 = 0.03125

sum all → 0.5 + 0.25 + 0 + 0.0625 + 0.03125 = 0.84375

1110.11011

_{(2)}= 14.84375

_{(10)}

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