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ECSE2610
Computer Components & Operations
(COCO)
Fall 2006
Part 6a
:
Synthesis of
Combinational Circuits
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View Full Document Manipulating Circuits
Given an algebraic representation of a logic
circuit, we manipulate the algebraic
representation to
Convert it to standard forms.
Redesign with more efficient gates like
NAND or NOR.
Simplify or even minimize the expression.
What is Minimization?
Minimization is the process of reducing a complex logic
expression or equation into its simplest form (with the
fewest number of terms) by removing redundancies and
terms having no effect on the output.
Similar to simplifying and reducing complex expressions
in Algebra by combining and collecting like terms.
As in algebraic reduction, rules must be followed that
guarantee the value of the expression is not changed by
the simplification.
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View Full Document Rationale for Logic Minimization
Reduce the complexity of the gate level implementation
Reduce the complexity of the gate level implementation
• Reduce the number of literals (gate inputs).
• Reduce the number of gates.
• Reduce the number of levels of gates.
• Reduce the number of literals (gate inputs).
• Reduce the number of gates.
• Reduce the number of levels of gates.
Fewer inputs implies faster gates in some technologies.
Fanins (number of gate inputs) are limited in some
technologies.
Fewer levels of gates implies reduced signal propagation
delays.
Minimum delay configuration often requires more gates.
Minimization Example
Apply the laws and theorems to simplify Boolean equations
Apply the laws and theorems to simplify Boolean equations
Example:
Full adder's carry out function
C
out
=
A' B C
in
+
A B' C
in
+
A B C
in
'
+
A B C
in
Simplify by minimizing the number terms
Simplify by minimizing the number terms
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View Full Document Recall the Combining Theorem I
A
B
F
A
B
G
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
X Y' + X Y = X(Y'+Y) = X
X Y' + X Y = X(Y'+Y) = X
F = A
B'
+ A
B
= A
G =
A'
B' +
A
B' = B'
Is there a systematic way of recognizing this pattern,
so we can use this theorem to simplify?
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This homework help was uploaded on 04/22/2008 for the course ECSE 2610 taught by Professor Ji during the Spring '08 term at Rensselaer Polytechnic Institute.
 Spring '08
 Ji

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