Question

Convert 15 from decimal to binary. Show your work.

Answer 1

Answer: 1111

Explanation: As a decimal number can be decomposed in a sum of products involving powers of ten, it can be factored as a sum of products of powers of 2 in order to convert to binary.

In the example, we can write 15 as a decimal number in this way:

1* 10¹ + 5* 10⁰ = 15

Decomposing in powers of 2:

1*2³ + 1* 2² + 1*2¹ + 1.2⁰ = 1 1 1 1 = (15)₂