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Binary Number Division
⇨ Binary division is similar to decimal division. The only difference is
that in decimal system, since we are dividing traditional numbers, the
dividend (or portion of it) can be 0, 1 or more than 1 times of the
divisor. However in binary, it can only be 0 or 1 times, i.e. the
dividend(or portion of it) is >= or < than the divisor.
⇨ Example: Let’s try dividing 6 by 3. Binary of 6 is 110 and that or 3 is
11 Following decimal division.
⇨ Convention We check for a portion of dividend from its left that is
>= the divisor. Then we subtract the multiple of the divisor that is
<= the portion of the dividend. The multiplier (1) gets appended to the
quotient and result of the subtraction is the remainder. We bring down 1
bit at the time (going left to right) for the remaining portion of the
dividend and check if the expression (remainder + brought down bit) is
>= the divisor. If not, we append 0 to the quotient, or else we follow
step 2 again.
⇨ The steps for 6 / 3 or 110 / 11 are
1 1 ] 1 1 0 [ 10
- 1 1
-----------
0 0 0
-----------
⇨ Quotient =1 0
⇨ Dividend =1 1 0
⇨ Reminder = 0
⇨ Divisor=1 1
⇨ Is 1 (left most bit of 110) >= 11. No (we don’t need to
add 0 to quotient here since 0s on the left are
insignificant).
⇨ Is 11 (left 2 most bits of 110) >= 11. Yes. We add 1 (multiplier) to
the quotient, and subtract 11 from 11. That gives us a remainder of 0.
Note, we are subtracting “one-one from one-one NOT eleven from
eleven”.
⇨ Now we bring down the remaining bit (0) from 110. Is 0 >= 11. No. So
we append 0 to the quotient.
⇨ Since we have no more bits remaining in the dividend, we stop here and
check. Our remainder is 0 and quotient is 10 (binary) = 2.