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The decimal value $0.25$

1. is equivalent to the binary value $0.1$
2. is equivalent to the binary value $0.01$
3. is equivalent to the binary value $0.00111$
4. cannot be represented precisely in binary

### 1 comment

$A)\ 0.\dfrac{1}{2^1}=0.5$

$B)\ 0.\dfrac{1}{2^2}=0.25\ \checkmark$

$C)\ 0.\dfrac{7}{2^5}=0.21875$

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First Multiplication Iteration

Multiply $0.25$ by $2$

$\begin{array}{c c c}0.25 \ast 2 = 0.50\;\text{(Product)} & \text{Fractional part} = 0.50 & \text{Carry} = 0 \textbf{ (MSB)} \end{array}$

Second Multiplication Iteration

Multiply $0.50$ by $2$

$\begin{array}{c c c}0.50 \ast 2 = 1.00\;\text{(Product)} & \text{Fractional part} = 1.00 & \text{Carry} = 1 \textbf{ (LSB)} \end{array}$

The fractional part in the $2$nd iteration becomes zero and hence we stop the multiplication iteration.

Carry from the $1$st multiplication iteration becomes MSB and carry from $2$nd iteration becomes LSB.

So the result is $0.01$

0.25 = 1/4

we can represent 1/4 with 2^(-2)  = 0.01