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
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Chapter 3: Combinational Circuits
Full Adder Circuit
s = a b cin.
Simplifying the Full Adder Circuit
Cout = ab + acin + bcin
Carry Look-Ahead Adder (CLA)
gi = aibi
pi = ai + bi
ci+1 = gi + pici
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
Building a 16 to 4 Encoder
Binary Coded Decimal (BCD) Encoder
Encoders and Decoders
Implementing a Boolean Function using an Decoder
F(x,y,z) = m( 1, 2, 5, 7 )
Multiplexers and Demultiplexers
Implementing a Boolean Function using a Multiplexer
G(x,y,z) = m( 1, 4, 5, 6 )
Multiplexer as a Full-Adder
Designing a 2-Bit Magnitude Comparator
Voting Logic Circuit
Light Emitting Diode (LED) Displays
BCD to 7-Segment Display Function Table