3.13 [20] <$3.3> Using a table similar to that shown in Figure 3.6, calculate the product of the hexadecimal unsigned 8-bit integers 62 and 12 using the hardware described in Figure 3.5. You should show the contents of each register on each step. Chapter 3 Arithmetic for Computers Multiplicand 32 bits 32-bit ALU Shift right Control Product Write test 64 bits FIGURE 3.5 Refined version of the multiplication hardware. Compare with the first version in Figure 3.3. The Multiplicand register, ALU, and Multiplier register are all 32 bits wide, with only the Product register left at 64 bits. Now the product is shifted right. The separate Multiplier register also disappeared. The multiplier is placed instead in the right half of the Product register. These changes are highlighted in color. (The Product register should really be 65 bits to hold the carry out of the adder, but it's shown here as 64 bits to highlight the evolution from Figure 3.3.) 3.3 Multiplication Iteration Step Multiplier Multiplicand Product Initial values 0011 0000 0010 0000 0000 1 1a: 1 Prod Prod + Mcand 0011 0000 0010 0000 0010 2: Shift left Multiplicand 0011 0000 0100 0000 0010 3: Shift right Multiplier 0001 0000 0100 0000 0010 2 1a: 1 Prod Prod + Mcand 0001 0000 0100 0000 0110 2: Shift left Multiplicand 0001 0000 1000 0000 0110 3: Shift right Multiplier 0000 0000 1000 0000 0110 3 1: 0 No operation 0000 0000 1000 0000 0110 2: Shift left Multiplicand 0000 0001 0000 0000 0110 3: Shift right Multiplier 0000 0001 0000 0000 0110 4 1: 0 No operation 0000 0001 0000 0000 0110 2: Shift left Multiplicand 0000 0010 0000 0000 0110 3: Shift right Multiplier 0000 0010 0000 0000 0110 FIGURE 3.6 Multiply example using algorithm in Figure 3.4. The bit examined to determine the next step is circled in color.