1. Computing Machinery Chapter 3: Combinational Circuits

3. Half Adder

4. Full Adder

5. Full Adder Circuit

6. Simplifying the Full Adder Circuit C out = ab + ac in + bc in s = a b c in. + +

7. N-Bit Adder

8. Ripple-Carry Adder

9. g i = a i b i p i = a i + b i c i+1 = g i + p i c i Carry Look-Ahead Adder (CLA) c in bibi aiai ith FA sisi c i+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?

10. Carry-Out Bits Circuit for CLA

11. Four-Bit CLA Circuit

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

13. Encoders

14. Building a 16 to 4 Encoder

15. Binary Coded Decimal (BCD) Encoder Function Table

16. Encoders and Decoders

17. 3-to-8 Decoder (aka 1-of-8)

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

19. Multiplexers and Demultiplexers

20. 4-to-1 Multiplexer

21. 1-to-4 Demultiplexer

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

23. Multiplexer as a Full-Adder

24. Magnitude Comparators

25. Designing a 2-Bit Magnitude Comparator

26. Voting Logic Circuit

27. Light Emitting Diode (LED) Displays

28. BCD to 7-Segment Display Function Table