Question

Using a table similar to that shown in Figure 3.10, Calculate 74 divided by21 using the hardware described in Figure 3.8. You should show the contents of each register on each step. Assume both inputs are unsigned 6-bit integers.

Short answer

The value of 74 divided by 21 is :

Quotient 3 Remainder 9

Step-by-step solution

Determine the MIPS Division algorithm

The division starts by subtracting the divisor register from the remainder register. The result will be placed in a Remainder register. Then, the remainder value will be checked. If the remainder value is greater than or equal to 0, the quotient register will be shifted to the left and set 1 to the rightmost bit. If the remainder value is less than zero, then the original value will be restored by adding the divisor and remainder. Also, the quotient register will shit to left and set the least significant bit to 0. The divisor register will be shifted to the right 1 bit. Finally checks for number of repetitions.

Determine the value of division in table format. 

Given that 74 is divided by 21. Convert both the values to binary.

$$\begin{gathered} {74}_{16}={01110100}_2 \\ {21}_{16}={00100001}_2 \end{gathered}$$

Rewrite them in 3 bits order:

$$\begin{gathered} {74}_{16}=000000111{100}_2 \\ {21}_{16}=010001000{000}_2 \end{gathered}$$

Division table is as follows:

Step	Action	Quotient	Divisor	Remainder
0	Initial values	000 000	010 001 000 000	000 000 111 100
1	remainder=remainder-Divisor	000 000	010 001 000 000	101 111 111 100
Remainder<0,R+D,Q left shift	000 000	010 001 000 000	000 000 111 100
Rshift Div	000 000	001 000 100 000	000 000 111 100
2	remainder=remainder-Divisor	000 000	001 000 100 000	111 000 011 100
Remainder<0,R+D,Q left shift	000 000	001 000 100 000	000 000 111 100
Rshift Div	000 000	000 100 010 000	000 000 111 100
3	remainder=remainder-Divisor	000 000	000 100 010 000	111 100 101 100
Remainder<0,R+D,Q left shift	000 000	000 100 010 000	000 000 111 100
Rshift Div	000 000	000 010 001 000	000 000 111 100
4	remainder=remainder-Divisor	000 000	000 010 001 000	111 110 110 100
Remainder<0,R+D,Q left shift	000 000	000 010 001 000	000 000 111 100
Rshift Div	000 000	000 001 000 100	000 000 111 100
5	remainder=remainder-Divisor	000 000	000 001 000 100	111 111 111 000
Remainder<0,R+D,Q left shift	000 000	000 001 000 100	000 000 111 100
Rshift Div	000 000	000 000 100 010	000 000 111 100
6	remainder=remainder-Divisor	000 000	000 000 100 010	000 000 011 010
Remainder>0,R+D,Q Lshift 1	000 001	000 000 100 010	000 000 011 010
Rshift Div	000 001	000 000 010 001	000 000 011 010
7	remainder=remainder-Divisor	000 001	000 000 010 001	000 000 001 001
Remainder>0,R+D,Q Lshift 1	000 011	000 000 010 001	000 000 001 001
Rshift Div	000 011	000 000 001 000	000 000 001 001

Now, convert the binary values to decimals:

$$\begin{gathered} Quotient={000011}_2=3 \\ Remainder={000000001001}_2=9 \end{gathered}$$

Therefore, the quotient and remainder of the 74 divided by 21 is 3 and 9 respectively.