Assignment

Exercise 1

• Answer these questions:

(a) How does the ALU know which function to perform?
(b) Explain clearly how the fetch-decode-execute cycle works. (What are its steps? Explain each step)
(c) Why is it that if MARIE has 4K words of main memory, addresses must have 12 bits?
(d) What is an opcode?
(e) Explain the functions of all of MARIE's registers.
(f) Explain each step the the MARIE instruction STORE performs.
(g) Describe how an interrupt works and name four different types.

Exercise 2

A digital computer has a memory unit with 24 bits per word. The instructions set consists of 150 different operations. All instructions have an operation code part (opcode) and an address part (allowing for only one address). Each instruction is stored in one word memory.

a) how many bits are needed for the opcode?
b) how many bits are left for the address part of the instruction?
c) what is the maximum allowable size for memory?
d) what is the largest unsigned binary number that can be accommodated in one word memory?

Exercise 3

A digital computer has a memory unit with 32 bits per word. The instruction set consists of 110 different operations. All instructions have an operation code part (opcode) and two address fields: one for a memory address and one for a register address. This particular system includes eight general-purpose, user-addressable registers. Registers may be loaded directly from memory and memory may be updated directly from the registers. Direct memory-to-memory data movement operations are not supported. Each instruction is stored in one word of memory.

a) how many bits are needed for the opcode?
b) how many bits are needed to specify the register?
c) how many bits are left for the memory address part of the instruction?
d) what is the maximum allowable size for memory?
e) what is the largest unsigned binary number that can be accommodated in one word of memory?

Exercise 4

Consider the MARIE program below.
a) list the hexadecimal code for each instruction.
b) draw the symbol table.
c) what is the value stored in the AC when the program terminates?

hex address    label     instructions
100                start,   LOAD A
101                           ADD B
102                           STORE D
103                           CLEAR
104                           OUTPUT
105                           ADDI D
106                           STORE B
107                           HALT
108                A,        HEX  00FC
109                B,        14-Dec
10A                C,        HEX 0108
10B                D,        HEX 0000

Exercise 5

Consider the MARIE program below.

a) list the hexadecimal code for each instruction.
b) draw the symbol table.
c) what is the value stored in the AC when the program terminates?

hex address     label     instructions
200                 begin,   LOAD base
201                            ADD Offs
202                 loop,    SUBT One
203                            STORE Addr
204                            SKIPCOND 800
205                            JUMP Done
206                            JUMPI Addr
207                            CLEAR
208                 done,   HALT
209                 base,   HEX 200
20A                Offs,    9-Dec
20B                One,    HEX 0001
20C                Addr,   HEX 0000

Exercise 6

Write the following code segment in MARIE's assembly language:

If x>1 then
Y=x+x;
X=0;
Endif;
Y=y+1;

Exercise 7

If x<=y then
Y=y+1;
Else if x !=z
Then y=y-1;
Else z=z+1;

Exercises 8

For guidance, look at Exercises 1 a & B and their solutions on page 835.

SHOW YOUR INTERMEDIATE COLUMNS that lead you to the final column solution.

Construct a truth table for:

a) xyz + x(yz)' + x'(y + z) + (xyz)'

b) (x + y') (x' + z') (y' + z')

Exercise 9

Is the fallowing true or false? Prove your answer.

(x XOR y)' = xy + (x + y)'

Exercises 10

Show that x = xy + xy'

a) using truth tables
b) Using Boolean identities

Exercise 11

Show that xz = (x + y) (x + y') (x' + z)

a) Using truth table
b) Using Boolean identities

Exercise 12

Use any method to prove the fallowing either true or false.
xz + x'y' + y'z' = xz + y'

Exercise 13

The truth table for a Boolean expression is shown below. Write the Boolean expression in sum of products form. (table is depicted below)

Exercise 14

Answer it and show the Truth Table for the one you selected.

Which of the fallowing Boolean expressions is not logically equivalent to all the rest?
a) wx' + xy' + xz
b) w + x' + y' + z
c) w(x' + y' + z)
d) wx'yz' + wx'y' + xy'y' + wz

Exercise 15

Given the Truth Table for (xz) + y'

state its Sum of Products expression

then draw the Logic Circuit for that Sum of Products.

xz + x'y' + y'z' = xz + y'

Exercise 16

Find the truth table that describe the following circuit:

Exercise 17

Find the truth table that describe the following circuit: