Binary division, like decimal division, is a method to divide one binary number (the dividend) by another (the divisor). Here's a breakdown of the process:
Steps for Binary Division
The fundamental steps of binary division are very similar to long division with decimal numbers:
- Compare the divisor with the dividend.
- Start by looking at the leftmost bits of the dividend.
- Check if the divisor is smaller than or equal to the current portion of the dividend you are comparing.
- If the divisor is smaller than or equal:
- Write a "1" in the quotient.
- Subtract the divisor from that portion of the dividend.
- The result of this subtraction becomes your new remainder.
- If the divisor is larger:
- Write a "0" in the quotient.
- Bring down the next number bit from the dividend portion and perform the step 1 again.
- Repeat the same process until the remainder becomes zero or the whole dividend is divided.
- Continue steps 1-3, bringing down the next bit of the dividend, if required.
- The division is complete when either the remainder is zero, or there are no more bits to bring down from the dividend. The remainder is then your fractional part (or leftover).
Example
Let’s take an example: Divide 10110 by 11:
| Step | Operation | Quotient | Remainder | Explanation |
|---|---|---|---|---|
| 1 | 11 into 10? | 0 | 10 | Divisor (11) is larger than the first two bits of dividend (10). So quotient is 0. Bring the next bit down. |
| 2 | 11 into 101? | 1 | 101-11=10 | Divisor (11) is smaller than 101 so quotient is 1. Then we perform the subtraction: 101-11 = 10. |
| 3 | 11 into 101? | 1 | 101-11=10 | Divisor (11) is smaller than 101 so quotient is 1. Then we perform the subtraction: 101-11 = 10. |
| 4 | Bring down the next 0 | 11 | 100 | Bring down the next bit of the dividend and you're evaluating 11 into 100, which gives you quotient 1. |
| 5 | 11 into 100? | 1 | 1 | Divisor (11) is smaller than 100 so quotient is 1. Then we perform the subtraction: 100 - 11 = 1 |
Therefore, 10110 divided by 11 is 110 with a remainder 1 (or 110.0011 if continued).
The quotient is 110, and the remainder is 1.
Key Points
- Binary Subtraction: Remember the rules for binary subtraction: 0 - 0 = 0, 1 - 0 = 1, 1 - 1 = 0, and 0 - 1 = 1 (borrow 1).
- Place Values: Each bit in binary has a place value that is a power of 2 (from right to left): 2⁰, 2¹, 2², 2³, and so on.
- Repeat: The repetitive nature of the process makes it easier once you understand the initial comparison and subtraction steps.
Binary division might seem complex at first, but with practice, it becomes straightforward. By mastering these steps, you can perform binary division efficiently.
