Question

The decimal equivalent of the binary number ${\left(1111001101\right)}_2$ is

• A. ${\left(970\right)}_{10}$
• B. ${\left(973\right)}_{10}$
• C. ${\left(975\right)}_{10}$
• D. None of these

Answer 1

The correct option is B

${\left(973\right)}_{10}$

Finding the decimal equivalent:

Given the binary number ${\left(1111001101\right)}_2$

To find the equivalent decimal number, multiply each term of the binary number by $2^n$ where $n$ is the corresponding place value of the binary number and then, sum all the terms.

Hence,

${\left(1111001101\right)}_2=2^9\times 1+2^8\times 1+2^7\times 1+2^6\times 1+2^5\times 0+2^4\times 0+2^3\times 1+2^2\times 1+2^1\times 0+2^0\times 1$

$=512+256+128+64+8+4+1$

$=973$

Hence the decimal equivalent of the binary number ${\left(1111001101\right)}_2$ is $973$.

Thus, option (B) is the correct answer.