Review: Multiplexer

1. Review: Multiplexer Sangkyum Kim (Sang) 2/16/2007

2. Announcements • HW2 due extended by today (2/16) at 5pm. • HW 3 is released • Due at 5:00pm on 2/21/2007 (Wed) • No late homework accepted • Check your EWS account • Non-engineering students taking Engineering classes are NOT given EWS accounts by default

3. Agenda • Multiplexer revisit • Quiz • Homework3

4. Multiplexer - General • A 2n-to-1 multiplexer takes: • nselect lines • 2ndata input lines • makes: • 1 output

5. Efficient implementation • We can actually implement a function with 3 variables with just one 22-to-1 mux, instead of an 23-to-1. n variables  2n-1 -to-1 multiplexer

6. What’s inside? • How to use AND gates and OR gates to implement an 8-1 multiplexer. • An NAND gates implementation of an 8-1 multiplexer.

7. DecoderMultiplexer • Can you use decoders and basic gates to make a multiplexer? Selector 1 Selector 0 Input 3 Input 2 Input 1 Input 0 Output

8. Quiz – Quiz 7: Question 2 You can write the expression for multiplexer(s) by truth table Truth Table K-Map Expression

9. Quiz – Quiz 7: Question 2 You can also find the expression for multiplexer(s) directly using boolean algebra. h = z’y’ + zx f = (z’)’y + z’h = zy + z’(z’y’ + zx) = zy + z’y’ g = y’h’ + yx’ = y’(z’y’ + zx)’ + yx’ = y’(z+y)(z’+x’) + yx’ = y’zx’ + yx’ = x’y + x’z

10. Quiz – Quiz 7: Question 3 • Use multiplexer in the efficient way without using invertors. What can you do to change the situation? Use other variables as the selectors.

11. Quiz – Quiz 7: Question 4 • The same question as before!