bit manipulation - Implement division with bit-wise operator

Question

How can I implement division using bit-wise operators (not just division by powers of 2)?

Describe it in detail.

Answer 1

The standard way to do division is by implementing binary long-division. This involves subtraction, so as long as you don't discount this as not a bit-wise operation, then this is what you should do. (Note that you can of course implement subtraction, very tediously, using bitwise logical operations.)

In essence, if you're doing Q = N/D:

1. Align the most-significant ones of N and D.
2. Compute t = (N - D);.
3. If (t >= 0), then set the least significant bit of Q to 1, and set N = t.
4. Left-shift N by 1.
5. Left-shift Q by 1.
6. Go to step 2.

Loop for as many output bits (including fractional) as you require, then apply a final shift to undo what you did in Step 1.