1. And Decoders Prof. Sin-Min Lee Department of Computer Science
Lecture 7
Multiplexors
And Decoders
Prof. Sin-Min Lee
Department of Computer Science

3. Two-Level NAND Gate Implementation
Example 1  

4. Two-Level NAND Gate Implementation
Example 1  

6. Design Procedure
Determine the required number of inputs and outputs and assign letter symbols to them.
Derive the truth table that defines the required relationship between inputs and outputs.
Obtain the Boolean function.
Draw the logic diagram.
Verify the correctness of the design.

7. Example
Design a circuit that converts a BCD codeword to its corresponding excess-3 codeword. We need 4 input variables and 4 output variables. Let us designate the 4 input binary variables by the symbols A, B, and C and D, and the four output variables by w, x, y, and z. The truth table relating the input and output variables is shown below:

8. Note that the outputs for inputs 1010 through 1111 are don't care.

11. Two-Lvel NOR Gate Implementation
Example 2   e

14. Richard Hamming
Richard Wesley Hamming, mathematician, pioneer computer scientist, and professor, died of a heart attack on January 7, 1998, in Monterey, California, at the age of 82. His research career began at Bell Laboratories in the 1940s, in the early days of electronic computers, and included the invention of the Hamming error-correcting codes. In the 1970s he shifted to teaching, and at his death he was Distinguished Professor Emeritus of computer science at the Naval Postgraduate School. He is survived by his wife Wanda, a niece, and a nephew.

15. Let us play a game ! A volunteer from the audience?
Pick a number, any number, between 1 and 50

16. Is the Number in Here?

17. Is the Number in Here?

18. Is the Number in Here?

19. Is the Number in Here?

20. Is the Number in Here?

21. Is the Number in Here?

22. And the Number is ….

24. 1948: Error Correction
Error-detecting coding, first developed for telephone switching, is now used throughout the computing and telecommunications industries. In 1948 , R.W. Hamming (left) of Bell Labs developed a general theory for error-correcting schemes in which "check-bits" are interspersed with information bits to form binary words in patterns. When a single error occurs in transmission, the word becomes invalid, but the error is automatically located and corrected.

50. Multiplexers
A combinational circuit that selects info from one of many input lines and directs it to the output line.
The selection of the input line is controlled by input variables called selection inputs.
They are commonly abbreviated as “MUX”.

53. Combinational circuit implementation using MUX
We can use Multiplexers to express Boolean functions also.
Expressing Boolean functions as MUXs is more efficient than as decoders.
First n-1 variables of the function used as selection inputs; last variable used as data inputs.
If last variable is called Z, then each data input has to be Z, Z’, 0, or 1.

57. Karnaugh Map Method of Multiplexer Implementation
Consider the function:
A is taken to be the data variable and B,C to be the select variables.

58. Example of MUX combo circuit
F(X,Y,Z) = Sm(1,2,6,7)