Question

Convert number system : ${\left(10101101\right)}_2={(.....................)}_{10}$

Answer 1

Converting given binary number $10101101$to decimal:

Multiply all the digits of the binary number by the corresponding power of two

${\left(10101101\right)}_2=(1\times 2^7)+(1\times 2^6)+(1\times 2^5)+(1\times 2^4)+(1\times 2^3)+(1\times 2^2)+(1\times 2^1)+(1\times 2^0)$

$=(1\times 128)+(1\times 64)+(1\times 32)+(1\times 16)+(1\times 8)+(1\times 4)+(1\times 2)+(1\times 1)$

$$\begin{gathered} =128+0+32+0+8+4+0+1 \\ =173 \end{gathered}$$

Therefore, ${\left(10101101\right)}_2={\left(173\right)}_{10}$

Hence, Option ‘B’ is Correct.