1. CSE 140 : Components and Design Techniques for Digital Systems
Discussion Session 3
Mihir Patankar

2. Midterm review Transistors and Logic gates Boolean Algebra SOP, POS
K-maps and logic minimization
COMBINATION OF THESE !!!

3. Transistors and Logic gates Gates and transistors NOT NAND

4. Boolean Algebra Summary
De Morgan’s Theorem
(A+B+C+ …..)’ = A’ . B’ . C’ + ……
(A.B.C. …..)’ = A’ + B’ + C’ + ...
Consensus Theorem
AB + A’C + BC = AB + A’C

5. Practice Problem (Boolean Algebra + Transistors)
Find output Q. Simplify using boolean algebra. Draw simplified circuit using NOR gates and INVERTERS only.

6. k-maps Intuitive way to simplify boolean equations with few variables
Just another way of representing the truth table in a grid
Helps grouping and logic simplification

7. Practice Problem (k-map + SOP + POS)
F(A,B,C,D) = ∑m(1,2,4,5,7,11,15) + DC(0,8)
Implicants : Any VALID grouping of 1’s. ALL subcubes are implicants
Prime Implicants : Implicant which is NOT a part of any other subcube
Essential Prime implicants : Contains at least one 1 that cannot be combined by any other sub cube

8. SOP Minimisation
F(A,B,C,D) = A’C’ + A’B’D’ + BCD + ACD

9. POS Minimisation
F(A,B,C,D) = (A+B+C’+D’). (A’+C). (A’+D)

10. Some more practice problems !!

11. Homework 2 Problem 2
Simplify to minimal SOP : (a’ + c + d)(b + c + d)(a + b + c’)
Simplify to minimal POS : a’c+a’b’d+cd’

12. Word Problem
A logic network has three inputs (A, B, C) and one output (Z). In the following situations we set the output Z to either a logic zero or one:
1. The output Z is logic 1 when the binary value of ABC is greater than 3 and odd.
2. When the binary value of ABC is greater than 3 and even, Z is a logic 0
3. When the binary value of ABC is less than 3, the output Z follows the result of the expression B⊕C
4. Don’t care otherwise
Give truth table, canonical SOP, minimal SOP

13. MT Fall 15 : Problem 1 Consider following Boolean expressions:
F0=(x + y)(x' + y') + x'y' + xy
F1=xy’+x’y
F2=(x’+y)(x+y’)
Prove that F0=F1+F2 using Boolean algebra

14. MT Fall 15 : Problem 2
A car has a fuel level detector that outputs the current fuel level as a 3­bit binary number abc corresponding to values ranging from 000=empty to 111=full. Create a circuit that illuminates a “low fuel” indicator light by setting output L to 1 when the fuel level drops below level 3 (011 ­ not inclusive).
Give truth table, canonical SOP, minimal SOP