Problem 5 (15 points) Using a table similar to that shown in Figure 3.10, show the steps of dividing unsigned 12-bit integer 87 by unsigned 6-bit integer 17 using the hardware described in Figure 3.8.

Problem 6 (6 points) Calculate the time necessary to perform a multiplication of two 8-bit integers using the approach given in Figure 3.7, assuming that an adder takes 4 time units. You need to give a justification.

Please see figures below:

Mplier3.Mcand Mplier2 Mcand Mplier1 Mcand Mplier0 Mcand Mplier31.Mcand Mplier30 Mcand Mplier29 Mcand Mplier28 Mcand 32 bits 32 bits 32 bits 32 bits 32 bits 32 bits 1 bi1 bit bit1 bit 32 bits Product1 Product0 Product47..16 Product63 Product62 FIGURE 3.7 Fast multiplication hardware. Rather than use a single 32-bit adder 31 times, this hardware "unrolls the loop" to use 31 adders and then organizes them to minimize delay. Divisor Shift right 64 bits Quotient 64-bit ALU Shift left 32 bits Control test Remainder Write 64 bits FIGURE 3.8 First version of the division hardware. The Divisor register, ALU, and Remainder register are all 64 bits wide, with only the Quotient register being 32 bits. The 32-bit divisor starts in the left half of the Divisor register and is shifted right 1 bit each iteration. The remainder is initialized with the dividend. Control decides when to shift the Divisor and Quotient registers and when to write the new value into the Remainder register. Iteration Step Quotient Divisor Remainder Initial values 1: Rem Rem-Div 2b: Rem