# Karnaugh Maps (k maps) - NPRU

Karnaugh Maps (K maps) What are Karnaugh1 maps? Karnaugh maps provide an alternative way of simplifying logic circuits. Instead of using Boolean algebra simplification techniques, you can transfer logic values from a Boolean statement or a truth table into a Karnaugh map. The arrangement of 0's and 1's within the map helps you to visualise the logic relationships between the variables and leads directly to a simplified Boolean statement. Named for the American electrical engineer Maurice Karnaugh. 1 Karnaugh maps Karnaugh maps, or K-maps, are often used to simplify logic problems with 2, 3 or 4 variables. Cell = 2n ,where n is a number of variables For the case of 2 variables, we form a map consisting of 2 2=4 cells as shown in Figure A B 0 1 A B 0 0 AB A B 0 00 1 A B A B 1

01 Maxterm A 1 0 1 10 11 B 2 3 0 1 0 1 AB A B AB AB Minterm Karnaugh maps 3 variables Karnaugh map Cell = 23=8 C AB 00 01 0 0 2 10 6 4 A B C A BC ABC AB C 1

1 11 3 7 5 A B C A BC ABC AB C Karnaugh maps 4 variables Karnaugh map CD AB 00 01 11 10 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14

10 00 01 11 10 Karnaugh maps The Karnaugh map is completed by entering a '1(or 0) in each of the appropriate cells. Within the map, adjacent cells containing 1's (or 0s) are grouped together in twos, fours, or eights. Example 2-variable Karnaugh maps are trivial but can be used to introduce the methods you need to learn. The map for a 2-input OR gate looks like this: A 0 1 B A Y B A B Y 0 0 0 0 1 1 1 0 1 1

1 1 1 0 1 1 1 B A+B A Example A B C Y 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0

1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 AC C AB 00 0 1 1 1 01 11 10 1 1 1

B B AC Exercise Let us use Karnaugh map to simplify the follow function. F1 = m0+m2+m3+m4+m5+m6+m7 F2 = m0+m1+m2+m5+m7 Answer Exercise Given the truth table, find the simplified SOP and POS form. A B C Y 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1

0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 Exercise Design two-level NAND-gate logic circuit from the follow timing diagram. A B C D F Dont care term CD AB 00 01 11 10

X 00 01 11 10 AD X 1 X X X X Exercise Design logic circuit that convert a 4-bits binary code to Excess-3 code A B C D W X Y Z 0 0 0 0 0 0 1 1 0

0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1

1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0

0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 x x x x 1 0 1 1 x x x x

1 1 0 0 x x x x 1 1 0 1 x x x x 1 1 1 1 1 1 0 1 x X X X X x X x

## Recently Viewed Presentations

• Bacilli masses together. Bacilli resembling Chinese letters. Vibrios. These are small slightly curved rod measuring 3-4 μmin length by 0.5 μmin width. Most vibriosare motile with a single flagellum at one end. They show a rapid darting motility, e.g.
• Tensor Geometry Quadratic Forms Curvature and Geometric Measure Angular Measure Tensor Calculus Derivatives and Gradients Christoffel's Theorem, Ricci's Lemma Second Derivatives The Curvature of Space Bianchi's Identity The Einstein Tensor Tensors Used in Physics Physical Matrices Inertia Tensor Stress and...
• CSCI 1290: Comp Photo. Fall 2018 @ Brown University. James Tompkin. Many slides thanks to James Hays' old CS 129 course, along with all of its acknowledgements.
• Planner Policy. The daily planner is a tool to keep students and parents organized and informed! This is also a great communication tool for parents and teachers.
• Winlink use continues to grow, especially for EmComm. The Winlink Development Team continues to enhance capabilities to adapt to changing needs. Winlink has three modes of operation to send and receive messages, even if the Internet is down: RF connection...
• ProPartner-Portal-Silver-Zugriff. Deal-Registrierungsprogramm(ohne Extra-Rabatt) Rabatt auf Lizenzen für interne Nutzung. ... um den Gegenwert in Ihrer Landeswährung zu ermitteln. Neu 2% bei Neukunden. Neu 10 %. Seit 01.02.2013 Bestandteil ab Silber-Partner.
• Robert Agnew's General Strain Theory Robert Agnew laid the foundation for a general strain theory. Strain results from the removal of a positively valued stimuli or the presentation of negative stimuli. We all experience multiple strain throughout our lives, but...
• The standards for compilations and reviews of financial statements of non-public entities are called Statements on Standards for Accounting and Review Services (SSARS) Financial Statement Reviews Inquiry and analytical procedures are performed for each significant account balance Accountant does NOT...