# Binary Division

Division of binary numbers is simpler than division of decimal numbers.

Let us extend to a fractional binary representation with the point (or comma) separating powers of 2 with positive and negative exponents, so that e g

• 110.11 thus represents
• $1\times 2^2 + 1\times 2^1 + 0\times 2^0+1\times 2^{-1}+1\times 2^{-2} = 4 + 2 + 0 +\frac{1}{2}+\frac{1}{4} = 6\frac{3}{4}$ decimal.

Division by the binary number $10 (=2=2^1)$ is done by shifting the point one step to the left.

Division by the binary number $100 (=4=2^2)$ is done by shifting the point two steps 0 to the left.

Division by the binary number 1 followed by k zeros is done by shifting the point k steps to the left.

Let a be binary number named dividend to be divided by another (non-zero) binary number b named divisor to give the quotient q=a/b.

The digits of the quotient q can be computed successively from left with first non-zero digit equal to the digit of the largest one-digit number d such that

• d*b <a.

Then replace a by latex a-d*b and repeat the process to find the next non-zero digit of the quotient, and so on. This procedure is called long division.

To do: