Question

Convert the binary number 110011 into its decimal equivalent.

• A. 49
• B. 51
• C. 53
• D. 55

Hint:

A quick way to remember powers of 2 for conversions is to start with 1 on the right and keep doubling as you move left: ... 128, 64, 32, 16, 8, 4, 2, 1. Then, simply add up the values where a '1' appears in the binary number.

Answer 1

The Correct Option is B

To convert a binary number to its decimal equivalent, we multiply each binary digit by its corresponding power of 2 and sum the results. The powers of 2 start from 0 for the rightmost digit.
The binary number is 110011.
Let's write out the positional values:
$1 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0$
Calculate the values of the powers of 2:
$1 \times 32 + 1 \times 16 + 0 \times 8 + 0 \times 4 + 1 \times 2 + 1 \times 1$
Sum the results:
$32 + 16 + 0 + 0 + 2 + 1 = 51$.
Thus, the decimal equivalent of the binary number 110011 is 51.