Lecture14_d9974016-5182-41d8-b931-289da74f912c (2).pptx

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1. ESC201: Lecture 14 1

2. Implementation of a Function using Mux 2 A 2 variable function can be implemented with a 4:1 mux with 2 select lines: one-to-one correspondence x 1 x 2 1 1 1 1 1 1 1 1 Can we do better?

3. Implementation of a Function using Mux 3 A 2 variable function can be implemented with a 2:1 mux with 1 select line x 2 x 2 1 1 y = x 2 when x 1 = 0 1 1 1 1 y = x 2 when x 1 = 1

4. Implementation of a Function using Mux 4 A 3 variable function can be implemented with a 4:1 mux with 2 select lines x y z z 1 x y z F 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 F = z when xy = 00 F = when xy =01   F = 0 when xy = 10 F = 1 when xy = 11

5. Implementation of a Function using Mux 5 A 3 variable function can be implemented with a 4:1 mux with 2 select lines: not an unique implementation y z x 1 x F = 0 when yz = 00 F = x when yz =01 F = 1 when yz = 10 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 F = x when yz = 11

6. Mux Applications 6 Resource Sharing

7. Decoders Decodes an encoded information maps a smaller number of inputs to a larger set of outputs 7  

8. Decoders with ‘Enable’ input 8

9. Decoders in Vending Machine 9

10. Term Generator for SOP Expression of a Function 10 term

11. Implementation of a Function using Decoders Decoder allows a quick implementation No minimization, but lots of gates… 11

12. e c E A B Bigger Decoders 3 by 8 decoder using a 2 by 4 decoder 12 1 1 1 1 e c b a

13. De-Multiplexer 13 S 1 S y y 1 y 2 y 3 D 1 D 1 D 1 1 D Data

14. De-Mux vs Decoder Only difference is in name and application 14 S 1 S Y Y 1 Y 2 Y 3 D 1 D 1 D 1 1 D

15. Exercise: Multiplier 15 B 1 B A 1 A A B 1 A B A 1 B 1 A 1 B Multiplicand Multiplier Partial products C3 C2 C 1 C

16. Binary Multiplication of n-bit Numbers Circuit for multiplying 4 bit numbers Complications : How to add four bits and carry Circuit for left or right shifting? 16

17. Binary Division Circuit for division Complications : How to compare two numbers? Circuit for left and right shifting? 17

18. Comparator 18

19. Bit-wise Comparison 19 where x i = 1 only if the pair of bits in position i are equal (i.e., if both are 1 or both are 0).

20. Bit-wise Comparison 20   only if and   only if and       only if and both are false  

21. Comparator via Modular Approach 21