Chapter 5, Problem 26E

Explanation of Solution

Explanation:

The given mathematical expression is $\text{A}\text{=}\text{(B}\text{+}\text{C)}\text{×}\text{(D}\text{+}\text{E)}$.

The above expression is evaluated using instructions with required operands.

If the number of operands increases then, the instructions required to complete the task decreases.

Three-address machine:

The number of instructions can be accommodated is 3.

The first operand stores the output obtained whereas the second and the third operands stores the required input.

ADD and MUL are used for representing addition and multiplication operations respectively.

The given mathematical expression $\text{A}\text{=}\text{(B}\text{+}\text{C)}\text{×}\text{(D}\text{+}\text{E)}$ can be evaluated as follows,

ADD R1, B, C

ADD R2, D, E

MUL A, R1, R2

Here, the inputs stored in B and C is added and the output is stored in R1 and the inputs stored in D and E is added and the output is stored in R2. The values stored in R1 and R2 are multiplied and final output is stored in A.

Therefore, the mathematical expression $\text{A}\text{=}\text{(B}\text{+}\text{C)}\text{×}\text{(D}\text{+}\text{E)}$ is evaluated in three instructions.

Two-address machine:

The number of instructions can be accommodated is 2.

The first operand stores the output obtained whereas the second operand stores the required input.

ADD and MUL are used for representing addition and multiplication operations respectively and LOAD is used for loading the required value.

The given mathematical expression $\text{A}\text{=}\text{(B}\text{+}\text{C)}\text{×}\text{(D}\text{+}\text{E)}$ can be evaluated as follows

LOAD R1, B

ADD R1, C

LOAD R2, D

ADD R2, E

MUL R1, R2

STORE A, R1

Here, the operand B is loaded and the input is stored in R1. It is added with the value stored in the operand C and the output is stored R1. The operand D is loaded and the input is stored in R2. It is added with the value stored in the operand E and the output is stored R2. The values stored in R1 and R2 are multiplied and finally the result is stored in the operand A.

Therefore, the mathematical expression $\text{A}\text{=}\text{(B}\text{+}\text{C)}\text{×}\text{(D}\text{+}\text{E)}$ is evaluated in six instructions