Question

What is the decimal equivalent of the binary number $101010$?

• A. $20$
• B. $42$
• C. $22$
• D. $23$

Answer 1

The correct option is B

$42$

Explanation of correct option:

Binary to decimal conversation is obtained by multiplying $2$ to the power of base index along with the value at that index position.

Given binary number is $101010$.

To find the decimal equivalent of the binary number, multiply each digit of the binary number by the corresponding power of two and add.

$101010=2^5\left(1\right)+2^4\left(0\right)+2^3\left(1\right)+2^2\left(0\right)+2^1\left(1\right)+2^0\left(0\right)$

$\Rightarrow$ $101010=32\left(1\right)+16\left(0\right)+8\left(1\right)+4\left(0\right)+2\left(1\right)+1\left(0\right)$

$\Rightarrow$ $101010=32+0+8+0+2+0$

$\Rightarrow$ $101010=42$

Thus, the decimal equivalent of the binary number $101010$ is $42$.

Hence, the correct option is $B)42$.