# How to convert binary fractions to decimal ( fixed point arithmetics )

```Example for n = 110.101

Step 1: Conversion of 110 to decimal
=> 1102 = (1*22) + (1*21) + (0*20)
=> 1102 = 4 + 2 + 0
=> 1102 = 6
So equivalent decimal of binary integral is 6.

Step 2: Conversion of .101 to decimal
=> 0.1012 = (1*1/2) + (0*1/22) + (1*1/23)
=> 0.1012 = 1*0.5 + 0*0.25 + 1*0.125
=> 0.1012 = 0.625
So equivalent decimal of binary fractional is 0.625

Step 3: Add result of step 1 and 2.
=> 6 + 0.625 = 6.625```
```Example for n = 4.47 k = 3

Step 1: Conversion of 4 to binary
1. 4/2 : Remainder = 0 : Quotient = 2
2. 2/2 : Remainder = 0 : Quotient = 1
3. 1/2 : Remainder = 1 : Quotient = 0

So equivalent binary of integral part of decimal is 100.

Step 2: Conversion of .47 to binary
1. 0.47 * 2 = 0.94, Integral part: 0
2. 0.94 * 2 = 1.88, Integral part: 1
3. 0.88 * 2 = 1.76, Integral part: 1

So equivalent binary of fractional part of decimal is .011

Step 3: Combined the result of step 1 and 2.

Final answer can be written as:
100 + .011 = 100.011```
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