computing machinery chapter 3: combinational circuits
DESCRIPTION
Computing Machinery Chapter 3: Combinational Circuits. Half Adder. Full Adder. Full Adder Circuit. s = a b c in. +. +. Simplifying the Full Adder Circuit. C out = ab + ac in + bc in. N-Bit Adder. Ripple-Carry Adder. Carry Look-Ahead Adder (CLA). c in. a i. b i. g i = a i b i - PowerPoint PPT PresentationTRANSCRIPT
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Computing Machinery
Chapter 3: Combinational Circuits
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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
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Full Adder
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Full Adder Circuit
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Simplifying the Full Adder Circuit
Cout = ab + acin + bcin
s = a b cin. ++
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N-Bit Adder
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Ripple-Carry Adder
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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?
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Carry-Out Bits Circuit for CLA
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Four-Bit CLA Circuit
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Cascading 4-Bit Adders to Make a 16-Bit Adder
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Encoders
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Building a 16 to 4 Encoder
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Binary Coded Decimal (BCD) EncoderFunction Table
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Encoders and Decoders
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3-to-8 Decoder(aka 1-of-8)
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Implementing a Boolean Function using an Decoder
F(x,y,z) = m( 1, 2, 5, 7 )
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Multiplexers and Demultiplexers
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4-to-1 Multiplexer
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1-to-4 Demultiplexer
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Implementing a Boolean Function using a Multiplexer
G(x,y,z) = m( 1, 4, 5, 6 )
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Multiplexer as a Full-Adder
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Magnitude Comparators
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Designing a 2-Bit Magnitude Comparator
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Voting Logic Circuit
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Light Emitting Diode (LED) Displays
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BCD to 7-Segment Display Function Table