3.19 [30] <§3.4> Using a table similar to that shown in Figure 3.10, calculate 7

Question

3.19 [30] <§3.4> Using a table similar to that shown in Figure 3.10, calculate
74 divided by 21 using the hardware described in Figure 3.11. You should show
the contents of each register on each step. Assume A and B are unsigned 6-bit
integers. This algorithm requires a slightly different approach than that shown in
Figure 3.9. You will want to think hard about this, do an experiment or two, or else
go to the web to figure out how to make this work correctly. (Hint: one possible
solution involves using the fact that Figure 3.11 implies the remainder register can
be shifted either direction.)(Note: algorithmic and table example in text is not for the figured hardware the problem wants.)

Divisor 64 bits 64-bit ALU Shift right Shift left - ( Control Remainder Write- test 128 bits FIGURE 3.11 An improved version of the division hardware. The Divisor register, ALU, and Quotient register are all 64 bits wide, with only the Remainder register left at 128 bits. Compared to Figure 3.8, the ALU and Divisor registers are halved and the remainder is shifted left. This version also combines the Quotient register with the right half of the Remainder register. (As in Figure 3.5, the Remainder register should really be 129 bits to make sure the carry out of the adder is not lost.)

Explanation / Answer

Consider Dividend==> A = (74)10 =(1001010)2

Divisor ==> B = (21)10 =(0010101)2

-B = 110 1111
Steps:
   Start: Remainder = zeros with dividend
   Remainder = remainder << 1
   Left half remainder = Left half remainder – divisor
   If remainder > 0
i. <<1 and Ro=1
   If remainder < 0
i. Remainder left half = remainder left half + divisor;

ii. remainder <<1; Ro=0

After done this process from step 4 to 5 ( Seven repetitions)
If yes, Remainder left half = remainder left half >> 1
   If not, go back to step 4 and do it again to step 6

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