Question

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.

Short answer

The product of the hexadecimal unsigned 8-bit integers 62 and 12 using the hardware is as follows:

${62}_{16}\times {12}_{16}=6E{4}_{16}$

Step-by-step solution

Determine the Multiplication Algorithm:

In multiplication, the number to be multiplied is called multiplicand, and the number that multiplies the multiplicand is called the multiplier.

First, the multiplier will be checked for 0 and 1. If the multiplier is 0, then the left shift will be done for 1 bit in the multiplicand register. If the multiplier is 1, then the multiplicand will be added to the product and then the left shift will be done for 1 bit in the multiplicand register. Then Shift the multiplier register 1 bit to the right. Then the repetition numbers will be checked, if it is less than 32 it again works from first. If it has completed 32 repetitions then the result will be produced.

Determine the product of the hexadecimal unsigned 8-bit integers 62 and 12 

Refer Figure 3.5 in the book.

From Figure 3.5 , the multiplicand will be passed to 32-bit ALU. In ALU the bits are checked and then passed to the product register. The Product register has the multiplier that is on the right half. Now, the control test will make the shift and write operations.

The multiplication of ${62}_{16}\times {12}_{16}$can be calculated as follows:

First, convert into binary:

$$\begin{gathered} {62}_{16}={01100010}_2 \\ {12}_{16}={00010010}_2 \end{gathered}$$

Here 00010010 is the multiplier and 01100010 is the multiplicand

Iteration	Step	Multiplicand	Product	Multiplier
0	Initial Values	110 010	000 000	001 010
1	LSN=0, No operation	110 010	000 000	001 010
Right Shift Product	110 010	000 000	000 101
2	Product=Product+Multiplicand	110 010	110 010	000 101
Right Shit Multiplier	110 010	011 001	000 010
3	LSB=0 , No Operation	110 010	011 001	000 010
Right Shit Multiplier	110 010	001 100	100 001
4	Product=Product+Multiplicand	110 010	111 110	100 001
Right Shit Multiplier	110 010	011 111	010 000
5	LSB=0 , No Operation	110 010	011 111	010 000
Right Shit Multiplier	110 010	001 111	101 000
6	LSB=0 , No Operation	110 010	001 111	101 000
Right Shit Multiplier	110 010	000 111	110 100

Now, rewriting the product in 32 bits format is 0000 0110 1110 0100.

Convert 0000 0110 1110 0100 to hexadecimal.

${0000011011100100}_2=6E{4}_{16}$

So, the product of ${62}_{16}\times {12}_{16}$is $6E{4}_{16}$