Advanced Concepts in Digital Systems: Exclusive Logic Gates and Quine-McCluskey Method
This comprehensive guide overviews key concepts in digital systems, including exclusive OR (EXOR) and exclusive NOR (EXNOR) logic gates, along with their implementations and optimization techniques using K-maps. It discusses odd function applications and parity generators/checkers, and dives into the propagation delays in integrated circuits. Furthermore, the Quine-McCluskey method is detailed for minimizing Boolean expressions, providing a systematic approach to digital circuit design. Suitable for students and professionals in electrical engineering.
Advanced Concepts in Digital Systems: Exclusive Logic Gates and Quine-McCluskey Method
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Presentation Transcript
SYEN 3330 Digital Systems Chapter 2 -Part 8 SYEN 3330 Digital Systems
Exclusive OR/ Exclusive NOR SYEN 3330 Digital Systems
Tables for EXOR/ EXNOR SYEN 3330 Digital Systems
EXOR/EXNOR Extensions SYEN 3330 Digital Systems
EXOR Implementations SYEN 3330 Digital Systems
EXOR Implementations (Cont.) SYEN 3330 Digital Systems
Odd Function SYEN 3330 Digital Systems
Odd Function Implementation SYEN 3330 Digital Systems
K-Maps of ODD and EVEN SYEN 3330 Digital Systems
Parity Generators/Checkers SYEN 3330 Digital Systems
Integrated Circuits SYEN 3330 Digital Systems
Digital Logic Families SYEN 3330 Digital Systems
Compatibility SYEN 3330 Digital Systems
Propagation Delay SYEN 3330 Digital Systems
Propagation Delay Example SYEN 3330 Digital Systems
Positive and Negative Logic SYEN 3330 Digital Systems
Positive and Negative Logic SYEN 3330 Digital Systems
Positive and Negative Logic (Cont.) SYEN 3330 Digital Systems
Logic Conventions SYEN 3330 Digital Systems
Quine-McCluskey (tabular) method 1. Arrange all minterms in group such that all terms in the same group have the same # of 1’s in their binary representation. 2. Compare every term of the lowest-index group with each term in the successive group. Whenever possible, combine two terms being compared by means of gxi+gxi’=g(xi+xi’)=g. Two terms from adjacent groups are combinable if their binary representation differ by just a single digit in the same position (from all 1-cube). 3. The process continues until no further combinations are possible. The remaining unchecked terms constitute the set of PI. SYEN 3330 Digital Systems
# x1,x2,x3,x4 x1,x2,x3,x4 x1,x2,x3,x4 x1,x2,x3,x4 0 0 0 0 0 0 0 0 - 0 0 - 0 - 0 0 0 (0,1) (0,2) (0,8) - 0 0 - - 0 - 0 - - 0 1 - 1 - 1 (0,1,8,9) (0,2,8,10) (1,5,9,13) (5,7,13,15) 1 2 8 0 0 0 1 0 0 1 0 1 0 0 0 0 - 0 1 - 0 0 1 0 - 1 0 - 0 1 0 1 0 0 - 1 0 - 0 (1,5) (1,9) (2,6) (2,10) (8,9) (8,10) Using prime implicant chart, we can find essential PI 5 6 9 10 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 2 5 6 7 8 9 10 13 15 7 13 0 1 1 1 1 1 0 1 (5,7) (5,13) (6,7) (9,13) 0 1 - 1 - 1 0 1 0 1 1 - 1 - 0 1 (2,6) (6,7) (0,1,8,9) (0,2,8,10) (1,5,9,13) (5,7,13,15) 15 1 1 1 1 (7,15) - 1 1 1 (13,15) 1 1 - 1 Ex) f(x1,x2,x3,x4) = (0,1,2,5,6,7,8,9,10,13,15) SYEN 3330 Digital Systems
The reduced PI chart The essential PI’s are (0,2,8,10) and (5,7,13,15) . So, f(x1,x2,x3,x4) = (0,2,7,8) + (5,7,13,15) + PI’s Here are 4 different choices (2,6) + (0,1,8,9), (2,6) + (1,5,9,13) (6,7) + (0,1,8,9), or (6,7) + (1,5,9,13) 1 6 9 (2,6) (6,7) (0,1,8,9) (1,5,9,13) m1 m2 m3 m4 A PI pj dominates PI pk iff every minterm covered by pk is also covered by pj. pj pk (can remove) m1 m2 m3 m4 m5 p1 p5 Branching method p1 p2 p3 p4 p5 If we choose p1 first, then p3, p5 are next. p3 p4 p2 p3 Quine – McCluskey method (no limitation of the # of variables) SYEN 3330 Digital Systems
