Question

What is $(1001{)}_2$ equal to?

• A. $(5{)}_{10}$
• B. $(9{)}_{10}$
• C. $(17{)}_{10}$
• D. $(11{)}_{10}$

Answer 1

Answer: (B)

$(9{)}_{10}$

Step 1: Write down the binary number:

$1001$

Step 2: Multiply each digit of the binary number by the corresponding power of two:

$1\times 2^3+0\times 2^2+0\times 2^1+1\times 2^0$

Step 3: Solve the powers:

$1\times 8+0\times 4+0\times 2+1\times 1=8+0+0+1$

Step 4: Add up the numbers written above:

$8+0+0+1=9.$

This is the decimal equivalent of the binary number $1001.$

Thus we get $(1001{)}_2$ equal to $(9{)}_{10}$.