Question

$(10101101{)}_2=(................{)}_{10}$

• A. 137
• B. 173
• C. 170
• D. none of these

Answer 1

Answer: (B)

Let us do the step by step solution as follows:
Step 1: Write down the binary number: $10101101$
Step 2: Multiply each digit of the binary number by the corresponding power of two:
$\left(1\times 2^7\right)+\left(1\times 2^6\right)+\left(1\times 2^5\right)+\left(1\times 2^4\right)+\left(1\times 2^3\right)+\left(1\times 2^2\right)+\left(1\times 2^1\right)+\left(1\times 2^0\right)$
Step 3: Solve the powers:
$(1\times 128)+(1\times 64)+(1\times 32)+(1\times 16)+(1\times 8)+(1\times 4)+(1\times 2)+(1\times 1)$
Step 4: Add up the numbers written above:
$128+0+32+0+8+4+0+1=173$
Hence, $(10101101{)}_2=(173{)}_{10}$