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Computing Machinery Chapter 3: Combinational Circuits

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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Computing Machinery Chapter 3: Combinational Circuits

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  1. Computing Machinery Chapter 3: Combinational Circuits

  2. Half Adder

  3. Full Adder

  4. Full Adder Circuit

  5. s = a b cin. + + Simplifying the Full Adder Circuit Cout = ab + acin + bcin

  6. N-Bit Adder

  7. Ripple-Carry Adder

  8. Carry Look-Ahead Adder (CLA) cin ai bi 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? ith FA ci+1 si

  9. Carry-Out Bits Circuit for CLA

  10. Four-Bit CLA Circuit

  11. Cascading 4-Bit Adders to Make a 16-Bit Adder

  12. Encoders

  13. Building a 16 to 4 Encoder

  14. Binary Coded Decimal (BCD) Encoder Function Table

  15. Encoders and Decoders

  16. 3-to-8 Decoder (aka 1-of-8)

  17. Implementing a Boolean Function using an Decoder F(x,y,z) = m( 1, 2, 5, 7 )

  18. Multiplexers and Demultiplexers

  19. 4-to-1 Multiplexer

  20. 1-to-4 Demultiplexer

  21. Implementing a Boolean Function using a Multiplexer G(x,y,z) = m( 1, 4, 5, 6 )

  22. Multiplexer as a Full-Adder

  23. Magnitude Comparators

  24. Designing a 2-Bit Magnitude Comparator

  25. Voting Logic Circuit

  26. Light Emitting Diode (LED) Displays

  27. BCD to 7-Segment Display Function Table

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