Calculate the time necessary to perform a multiply using the approach given in Figures 3.3 and 3.4 if an integer is 8 bits wide and each step of the operation takes 4 time units. Assume that in step 1a an addition is always performed€”either the multiplicand will be added, or a zero will be. Also assume that the registers have already been initialized (you are just counting how long it takes to do the multiplication loop itself). If this is being done in hardware, the shift s of the multiplicand and multiplier can be done simultaneously. If this is being done in soft ware, they will have to be done one after the other. Solve for each case.

Figure 3.3

Figure 3.4

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Multiplicand Shift left 64 bits Multiplier Shift right 64-bit ALU 32 bits Product Control test Write 64 bits Start 1. Test Multipliero Multipliero = 1 Multipliero = 0 1a. Add multiplicand to product and place the result in Product register 2. Shift the Multiplicand register left 1 bit 3. Shift the Multiplier register right 1 bit No: < 32 repetitions 32nd repetition? Yes: 32 repetitions Done