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Topic Content:
- Binary Arithmetic Operations – Division
Binary division is straightforward and easy to understand if you follow simple rules.
Similar to the decimal number system, binary division follows the four-step process:
- Divide
- Multiply
- Subtract
- Bring down
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.)
Worked Example 2.5.1:
Solve the following:
a. 1110 ÷ 111
b. 1010 ÷ 10
c. 1101001 ÷ 101two
Solution
Divide the following numbers
a. 1110 ÷ 111
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.
If we added all the 0’s in the quotient the answer would have been 0010. Removing the first two 00’s does not change the value of the number. 0010two = 10two
Answer = 10two
2nd Method
Note: Both the binary and the decimal systems produce the same result.
1110two = 1 x 23 + 1 x 22 + 1 x 21 + 0 x 20
= 8 + 4 + 2 + 0 = 14
111two = 1 x 22 + 1 x 21 + 1 x 20
= 4 + 2 + 1 = 7
14 ÷ 7 = 2
From the long division method, the result we got was 10two
10two = 1 x 21 + 0 x 20 = 2 + 0 = 2
b. 1010 ÷ 10
Explanation:
10 is the divisor, 1010 is the dividend.
Compare the divisor (10) to the dividend (1010) from the first digit.
10 > 1 so we carry on (or add a 0)
10 = 10. This can be divided. We write 1 in the quotient.
We then multiply the divisor (10) by 1 then find the remainder by subtracting the result. (10 – 10 = 0)
The remainder is 0 and the number brought down is 1. What we have now is 01.
We then try and divide again. 10 > 01. This can’t be divided. We write 0 in the quotient.
We then bring down the next digit which is 0. We now have 10.
We then try and divide again. 10 = 10. This can be divided. We write 1 in the quotient.
Answer = 101two
c. 1101001 ÷ 101two
Answer = 10101two
