1. Abdullah Said Alkalbani alklbany@hotmail.com University of Buraimi
ECEN Digital Logic Design Lecture 5 Combinational logic circuit Analysis & Design (part1) Circuit Analysis Procedure
Abdullah Said Alkalbani
University of Buraimi

2. Important concept – analyze digital circuits
Overview
Important concept – analyze digital circuits
Given a circuit
Create a truth table
Create a minimized circuit
Approaches
Boolean expression approach
Truth table approach
Leads to minimized hardware
Provides insights on how to design hardware
Tie in with K-maps (next time)
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

3. The Problem
How can we convert from a circuit drawing to an equation or truth table?
Two approaches
Create intermediate equations
Create intermediate truth tables A B C C’
Out

4. Label Gate Outputs
Label all gate outputs that are a function of input variables.
Label gates that are a function of input variables and previously labeled gates.
Repeat process until all outputs are labelled. A B C C’
Out R S T

5. Approach 1: Create Intermediate Equations
Step 1: Create an equation for each gate output based on its input.
R = ABC
S = A + B
T = C’S
Out = R + T A B C C’
Out R S T

6. Approach 1: Substitute in subexpressions
Step 2: Form a relationship based on input variables (A, B, C)
R = ABC
S = A + B
T = C’S = C’(A + B)
Out = R+T = ABC + C’(A+B) A B C C’
Out R S T

7. Approach 1: Substitute in subexpressions
Step 3: Expand equation to SOP final result
Out = ABC + C’(A+B) = ABC + AC’ + BC’ A B C
Out A C’ B C’

8. Approach 2: Truth Table
Step 1: Determine outputs for functions of input variables. A 1 B C R S A B C C’
Out R S T

9. Approach 2: Truth Table
Step 2: Determine outputs for functions of intermediate variables. A 1 B 1 C 1 R 1 S T C’
T = S * C’ A B C C’
Out R S T

10. Approach 2: Truth Table Step 3: Determine outputs for function. A 1 B1 B C R S T
Out
R + T = Out A B C C’
Out R S T

11. More Difficult Example
Step 3: Note labels on interior nodes

12. More Difficult Example: Truth Table
Remember to determine intermediate variables starting from the inputs.
When all inputs determined for a gate, determine output.
The truth table can be reduced using K-maps. A 1 B 1 C 1 F2 1
F’2 1 T1 1 T2 1 T3 1 F1 1

13. Two approaches illustrated
Summary
Important to be able to convert circuits into truth table and equation form
WHY? ---- leads to minimized sum of product representation
Two approaches illustrated
Approach 1: Create an equation with circuit output dependent on circuit inputs
Approach 2: Create a truth table which shows relationship between circuit inputs and circuit outputs
Both results can then be minimized using K-maps.
Next time: develop a minimized SOP representation from a high level description
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.