CS147 Midterm Study Guide

Date: September 25, 2001

2001Fall :CS 147 First midterm study guide

2001Fall :CS 147 First midterm study guide

"I see and I forget, I hear and I remember, I do and I understand." -----------Confucius

Chapter 1 Combinational Logic

Truth tables, boolean algebra, logic equations
Gates: AND, OR, XOR, and inversion
Combinational logic

Decoders
Multiplexors
Creating a logic circuit to represent an arbitrary truth table. (Skip PLAs and Don't Cares)

Chapter 3 ISA

Sample Problems.

Consider the problem of adding two 2-bit binary numbers, producing a 3-bit sum.

Part A: Give the complete truth table for this function, without optimization.

Part B: Indicate the number of input not gates, row nand gates and output nand gates required to implement this function, without optimization.

A1 A0 B1 B0 | S2 S1 S0

--------------+---------

0 0 0 0 | 0 0 0

0 0 0 1 | 0 0 1

0 0 1 0 | 0 1 0

0 0 1 1 | 0 1 1

0 1 0 0 | 0 0 1

0 1 0 1 | 0 1 0

0 1 1 0 | 0 1 1

0 1 1 1 | 1 0 0

1 0 0 0 | 0 1 0

1 0 0 1 | 0 1 1

1 0 1 0 | 1 0 0

1 0 1 1 | 1 0 1

1 1 0 0 | 0 1 1

1 1 0 1 | 1 0 0

1 1 1 0 | 1 0 1

1 1 1 1 | 1 1 0

Part B: Indicate the number of gates required to implement this function, without optimization.

input not gates: 4

row nand gates: 16

output nand gates 3

For the Boolean function: F = XY + X'YZ of three inputs, list its minterms. Express F in the sum of minterms in algebraic form. List minterms of F'.

State if the following identities are TRUE or FALSE
b. (B' + C)(B' + D) = B' + CD
d. X'Z +X'Y + XZ = X'YZ' + X'YZ + X'Z
e. (P + Q' + R)(P + Q' + R') = Q' + PR' + RP'

Consider the following truth table:

         a  b  c    f
        --------------
         0  0  0    1
         0  0  1    0
         0  1  0    1
         0  1  1    0
         1  0  0    1
         1  0  1    1
         1  1  0    1
         1  1  1    0

Use this table to generate its corresponding function in the

canonical SOP form
canonical POS form
minimized SOP form
minimized POS form

Analyse the following circuit (generate both the algebraic representation and the truth table):