1. Digital Electronics

2. Chapter 4
Combinational Logic

3. Terminology
Combinational:Output is completely determined from the input(s) and does not depend on time
Sequential : Output depends on the input(s), previous history, and time
Analysis : A circuit is given and one must determine the Truth Table
Design: One must build a circuit whose output(s) are given as a Truth Table

4. Analysis Problem
Set up the Truth Table

5. Analysis: Truth Table
x y F

6. Design or Synthesis x y z F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0

7. K-Map of Design Problem
y'z' y'z yz yz' x' x 1 1 1 1
F = x y + x z + y z

8. Final Circuit Design
F = x y + x z + y z

9. Binary Adder Half Adder Truth Table x y C S 0 0 0 0 0 1 0 1 1 0 0 1

10. Implementation of Half Adder

11. Full Adder
x y z C S

12. Implementation of Full Adder

13. Magnitude Comparator

14. Comparator Theory
x is generated from XNOR and equals 1 if the two bits are equal
A = B if all the x’s are equal
A > B if the corresponding bit is greater as long as the previous bits are equal
A < B if the corresponding bit is smaller as long as the previous bits are equal

15. 3-to-8 Line Decoder

16. Decoder Truth Table
Which output will be high when x =1, y = 1 and z = 0 ?

17. Decoder Truth Table
Only line 6 will be high. The other 7 lines will be low.

18. Implement the Full Adder with a 3x8 Decoder
Decoder Application
Implement the Full Adder with a 3x8 Decoder

19. Full Adder using 3x8 Decoder

20. Important Note!
The actual 74LS138 decoder chip has inverted outputs … welcome to the REAL WORLD!!!

21. Multiplexer
A multiplexer is a combinational circuit that selects binary information from one of many input lines and directs it to a single output line.

22. Multiplexer

23. Multiplexer Application Implement the function F(x,y,z) = Σ(1,2,6,7)

24. F(x,y,z) = Σ(1,2,6,7) with a multiplexer

25. VHDL // A 2x4 Decoder with enable E module my_decoder (A,B,E,D);
input A,B,E;
output [0:3] D;
assign D[0] = ~(~A & ~B & ~E),
D[1] = ~(~A & B & ~E),
D[2] = ~(A & ~B & ~E),
D[3] = ~(A & B & ~E);
endmodule

26. Gate implementation of my_decoder

27. More VHDL ... //A 4-bit comparator module comp(A,B,ALTB,AGTB,AEQB);
input [3:0] A,B;
output ALTB,AGTB,AEQB;
assign ALTB = (A < B),
AGTB = (A > B),
AEQB = (A == B);
endmodule

28. That’s All Folks!