Division of Number Bases

Example 2.2.1:

Divide the following numbers:

a. 1110_two ÷ 111_two
b. 1010_two  ÷ 10_two
c. 1101001_two ÷ 101_two

Solution

The long division method is one of the most efficient and easiest ways to solve binary division.

Remember these rules

• The dividend is divided by the divisor, and the answer is the quotient.
• Compare the divisor to the first digit in the dividend. If the divisor is the larger number, keep adding digits to the dividend until the divisor is the smaller number. (For example, if calculating 156 ÷ 2, we would compare 2 and 1, note that 2 > 1, and compare 2 to 15 instead.)

a. 1110_two ÷ 111_two

Explanation

111 is the divisor, 1110 is the dividend.

Compare the divisor (111) to the dividend (1110) from the first digit.

111 > 1 so we carry on (or add a 0)
111 > 11 so we carry on (or add a 0)
111 = 111, This can be divided. We write 1 in the quotient.

Like standard division, we then multiply the divisor (111) by 1 and then find the remainder by subtracting the result.

The remainder is 0 and the number brought down is 0. What we have now is 00.

We then try and divide again. 111 > 00 so we add a 0 to the quotient.

0010_two = 10_two

Answer = 10_two

b. 1010_two  ÷ 10_two