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A lecture note from cs031 course on digital logic design. It introduces karnaugh maps as a manual and heuristic method to minimize the size of boolean circuits. How to draw and fill the karnaugh map with the truth table, cover 1s with boxes, and generate products for each box to obtain the minimal sum of products expression. The document also covers the concept of don't cares and their usage in simplifying boolean functions.
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CS031 Lecture 3 (b) (^) Page 1
Pascal Van Hentenryck Karnaugh Maps
Programming Language Assembly Language Machine Language Sequential Circuit Combinational Circuit Binary Value Voltage Programming Language Assembly Language Machine Language Sequential Circuit Combinational Circuit Binary Value Voltage
Minimizing Boolean Functions
The basic strategy
Another Presentation of a Truth Table The Karnaugh map looks like this What is the boolean function?
Another Simplification Problem
Another Simplification Problem
f(x,y,z) = x’yz + xy’z’ + xyz’ + xyz
By setting the left and right x’s to 1 we can make a 2x2 square, reducing the function to: f(x,y,z)=z’
What if the x’s were 0’s? f(w,x,y,z)=(w’x’y) + (w’xz) + (xyz)
f(w,x,y,z)=(w’x’y) + (w’xz) + (xyz)