1. COMPSCI 210 Semester 1 - 2015 Tutorial 2: Logic Gates

2. Review of Boolean algebra Example 1. Write the truth table for : B+(BA)=F(AB) ABABF(AB) 0000 0101 1000 1111 2

3. Exercise 1: write a “truth table” for: a) (x+y+z)(xyz) b) (XYZ) + (XY) (Z+Y) c) PT(P+Z) _ _ _ _ _ _ _ _ _ 3

4. Basic logic gates Not And Or Nand Nor Xor 4

5. NAND Gate NAND Z X Y Z 0 0 1 0 1 1 1 0 1 1 1 0 X Y Z = X.Y nand(Z,X,Y) W = X.Y Z = W = X.Y NOT-AND X Y Z W ____ _ 5

6. NOR Gate NOR X Y Z Z = (X + Y) nor(Z,X,Y) X Y Z 0 0 1 0 1 0 1 0 0 1 1 0 NOT-OR X Y W = X + Y Z = W = (X + Y) Z W _______ _ 6

7. Rosen, §10.3 question 1 Find the output of the following circuit Answer: (x+y)y x+yx+y y (x+y)y(x+y)y__ 7

8. Rosen, §10.3 question 2 Find the output of the following circuit Answer: xy x y xyxy _ _ ___ ___ 8

9. Rosen, §10.3 question 6 Write the circuits for the following Boolean algebraic expressions a) x+y __ __ x x+yx+y 9

10. Rosen, §10.3 question 6 Write the circuits for the following Boolean algebraic expressions b)(x+y)x _______ x+yx+y x+yx+y (x+y)x(x+y)x 10

11. Example Draw the circuit diagram to implement the expression 11

12. Create truth table for the following circuit: ABX 000 011 101 111 12

13. Exercise 2: Create truth table for the following circuit: 13

14. 14 Exercise 3: Draw the truth table for this decoder:

15. ABQ0Q1Q2Q3 001000 010100 100010 110001 Exercise 3 - Solution 15

16. De Morgan’s Theorem NOT all variables Change. to + and + to. NOT the result -------------------------------------------- (X + Y) = __________ (X. Y) = ______ __ _______ __ (X + Y) = X + Y X + Y = __ 16 __ X. Y

17. Memory A flip-flop holds a single bit of memory – The bit “flip-flops” between the two NAND gates In reality, flip-flops are a bit more complicated – Have 5 (or so) logic gates (transistors) per flip-flop Consider a 1 Gb memory chip – 1 Gb = 8,589,934,592 bits of memory – That’s about 43 million transistors! In reality, those transistors are split into 9 ICs of about 5 million transistors each 17