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ENGIN 112 Intro to Electrical and Computer Engineering Lecture 12 Circuit Analysis Procedure :

ENGIN 112 Intro to Electrical and Computer Engineering Lecture 12 Circuit Analysis Procedure

Overview:

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)

The Problem :

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 A B C’ Out

Label Gate Outputs :

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 A B C’ Out R S T

Approach 1: Create Intermediate Equations :

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 A B C’ Out R S T

Approach 1: Substitute in subexpressions :

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 A B C’ Out R S T

Approach 1: Substitute in subexpressions :

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

Approach 2: Truth Table :

Approach 2: Truth Table Step 1: Determine outputs for functions of input variables. A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 R 0 0 0 0 0 0 0 1 S 0 0 1 1 1 1 1 1 A B C A B C’ Out R S T

Approach 2: Truth Table :

Approach 2: Truth Table Step 2: Determine outputs for functions of intermediate variables. A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 T = S * C’ R 0 0 0 0 0 0 0 1 S 0 0 1 1 1 1 1 1 T 0 0 1 0 1 0 1 0 C’ 1 0 1 0 1 0 1 0 A B C A B C’ Out R S T

Approach 2: Truth Table :

Approach 2: Truth Table Step 3: Determine outputs for function. A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 R 0 0 0 0 0 0 0 1 S 0 0 1 1 1 1 1 1 T 0 0 1 0 1 0 1 0 Out 0 0 1 0 1 0 1 1 R + T = Out A B C A B C’ Out R S T

More Difficult Example :

More Difficult Example Step 3: Note labels on interior nodes

More Difficult Example: Truth Table :

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 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 F 2 0 0 0 1 0 1 1 1 F’ 2 1 1 1 0 1 0 0 0 T 1 0 1 1 1 1 1 1 1 T 2 0 0 0 0 0 0 0 1 T 3 0 1 1 0 1 0 0 0 F 1 0 1 1 0 1 0 0 1

Summary:

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

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