Question

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

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

Answer 1

Answer: (B)

173

Answer 2

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, $(10101101)_{2}=(173)_{10}$