Question

Convert the binary number 000001012 to decimal by adding the powers of 2:

A) 10
B) 18
C) 26
D) 36

Answer 1

The binary number 00000101 converts to the decimal number 5 by adding the powers of 2 for each position where there is the digit 1. In this case, we add 2 squared (4) and 2 to the power of zero (1) to get 5.

Step-by-step explanation:

To convert the binary number 00000101 to decimal, we add the powers of 2 corresponding to each digit's place from right to left, starting with 20. Each digit in the binary number represents a power of 2 depending on its position. If the digit is 1, we include its associated power of 2 in our sum; if it's 0, we do not.

The binary number 00000101 has 1s at the third and zeroth position from the right. This means we add 22 (which is 4) and 20 (which is 1). Therefore, the calculation will be 4 + 1 = 5.

Thus, the binary number 00000101 converts to the decimal number 5.