Question

Convert 110111001101 base 2 into base eight without transitioning through number numeral or base 10

Answer 1

(110111001101)₂ → (6715)₈

The given binary number is (110111001101)₂.

To convert it into octal (base 8), we group the decimal number in a group of 3, starting from the leftmost end.

So,

(110 111 001 101)₂

We know, (110)₂ = 0×2⁰ + 1×2¹ + 1×2² = 0 + 2 + 4 = (6)₈

Similarly (111)₂ = (7)₈

(001)₂ = (1)₈

(101)₂ = (5)₈

So, we get (6715)₈ as the octal representation of (110111001101)₂.