**3.3.2 UNSIGNED DIVISION**

In longhand binary division, we must successively attempt to subtract the divisor from the dividend, using the fewest number of bits in the dividend as we can.

Figure 3-13 illustrates this point by showing that (11)2 does not “ﬁt” in 0 or 01, but does ﬁt in 011 as indicated by the pattern 001 that starts the quotient.

Computer-based division of binary integers can be handled similar to the way that binary integer multiplication is carried out, but with the complication that the only way to tell if the dividend does not “ﬁt” is to actually do the subtraction and test if the remainder is negative. If the remainder is negative then the subtraction must be “backed out” by adding the divisor back in, as described below.

In the division algorithm, instead of shifting the product to the right as we did for multiplication, we now shift the quotient to the left, and we subtract instead of adding. When two n-bit unsigned numbers are being divided, the result is no larger than n bits.

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