Question

What is the base 8 representation of the number 11100111

Answer 1

If the given number is in base 2, that means

11100111₂ = 2⁷ + 2⁶ + 2⁵ + 2² + 2 + 1

8 = 2³, and so we have

11100111₂ = 2 • (2³)² + (2³)² + 2² • 2³ + 2² + 2 + 1

11100111₂ = 3 • 8² + 4 • 8 + 7

11100111₂ = 347₈

Because 8 is the 3rd power of 2, we can also split up the given number into block of length up-to 3, then convert each block directly into base 8:

11 100 111

11₂ = 2 + 1 = 3

100₂ = 2² = 4

111₂ = 2² + 2 + 1 = 7

so again we get 347₈.