EE141 Combinational Circuits 1 Chapter 6 Designing Combinational Logic Circuits November 2002.
Computing Machinery Chapter 3: Combinational Circuits
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Transcript of Computing Machinery Chapter 3: Combinational Circuits
Computing Machinery
Chapter 3: Combinational Circuits
Half Adder
a b
s
c
HalfAdder
a b
c s
a b
s
c
HalfAdder
a b
c s
a b
s
c
a b
s
c
HalfAdder
a b
c s
HalfAdder
a b
c s
Full Adder
Full Adder Circuit
Simplifying the Full Adder Circuit
Cout = ab + acin + bcin
s = a b cin. ++
N-Bit Adder
Ripple-Carry Adder
gi = aibi
pi = ai + bi
ci+1 = gi + pici
Carry Look-Ahead Adder (CLA)
cinbiai
ith FA
sici+1
1. Will ith FA generate a carry bit?
2. Will ith FA propagate a carry bit?
3. What is the carry-out for the ith FA?
Carry-Out Bits Circuit for CLA
Four-Bit CLA Circuit
Cascading 4-Bit Adders to Make a 16-Bit Adder
Encoders
Building a 16 to 4 Encoder
Binary Coded Decimal (BCD) EncoderFunction Table
Encoders and Decoders
3-to-8 Decoder(aka 1-of-8)
Implementing a Boolean Function using an Decoder
F(x,y,z) = m( 1, 2, 5, 7 )
Multiplexers and Demultiplexers
4-to-1 Multiplexer
1-to-4 Demultiplexer
Implementing a Boolean Function using a Multiplexer
G(x,y,z) = m( 1, 4, 5, 6 )
Multiplexer as a Full-Adder
Magnitude Comparators
Designing a 2-Bit Magnitude Comparator
Voting Logic Circuit
Light Emitting Diode (LED) Displays
BCD to 7-Segment Display Function Table