Lecture No. 14
Combinational Functional Devices
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Odd Parity Function - Digital Logic Design - Lecture Slides, Slides of Digital Logic Design and Programming
Odd Parity Function, SOP Expression Simplification, Simplifying Expression, Odd Parity Generator Circuit, Operation of Odd Parity circuit, XOR and XNOR Gates, Combinational Functional Devices are main points of this lecture.
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2011/2012
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Lecture No. 14
Combinational Functional Devices
Recap
Odd-Prime Number Detector Circuit
Using Quine-McCluskey Method
Combinational Logic
Implemented in SOP and POS form
Design and Implementation Steps
Timing Diagram
Active High/Low inputs/outputs
SOP Expression SImplification
D 3 D 2
D 1 D 0 00 01 11 10
00 1 0 1 0
01 0 1 0 1
11 1 0 1 0
10 0 1 0 1
Simplifying Expression
AB CD+ ABCD+ ABCD+ABCD+ABCD+ABCD+ABCD+ABC D
= AB ( CD+CD)+ AB(CD+CD)+ AB(CD+CD)+ AB(CD+CD )
= AB ( CD+CD)+ AB(CD+CD)+ AB(CD+CD)+ AB(CD+CD )
= ( CD +CD)(AB+ AB)+ (CD+CD)(AB+ AB )
= ( C ⊕D)(A⊕B)+(C⊕D)(A⊕B ) ( = X Y + XY = X⊕Y)
= ( A ⊕B)⊕(C⊕D )
Operation of Odd-Parity circuit
A
B
C
D
P
t0 t1 t2 t3 t4 t5 t6 t7 t
XOR & XNOR Gates
XOR function
XNOR function
AB + A B
AB + AB
XNOR Gate
A
B
F
Combinational Functional
Devices
Comparators
BCD to 7-Segment
Parity Generator Circuit
Half & Full Adders
A
B
Input Bits C out Output Bits
Half-Adder
A
B
Input BitsC in C out Output Bits
Full-Adder
Half-Adder
Function Table
Expression
Logic Circuit
Half-Adder Circuit
A
B
C out
Sum = AB+ AB = A ⊕ B CarryOut^ = AB
Full-Adder
Function Table
Expression
Logic Circuit
Sum Expression
Sum = ABC + ABC+ ABC + ABC
Sum = A(B C+BC) + A(BC+BC )
Sum = A(B ⊕C) + A(B⊕ C )
Sum = A ⊕B ⊕ C
Carry Out Expression
CarryOut = ABC + ABC + ABC + ABC
CarryOut = C( AB + AB) + AB(C+C )
CarryOut = C(A ⊕B) + AB