# Lec25

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## Lec25

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- Pages:
- 8
- School:
- Texas A&M University
- Course:
- Ecen 215 - Prin Of Electrical Engr

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ECEN 215 Principles of Electrical Engineering Dr Mina Rahimian Lecture 25 Date 11 25 13 Finding logic expression from the truth table There are two methods to find the the logic expression from the truth table Sum of products SOP Product of the sum POS Sum of products In this method we select the rows with the output of 1 and find the corresponding logical combinations at the input Product of the sum In this method we select the rows with the output of 0 which gives the expression for the inverted output and find the corresponding logical combinations for that Then use DeMorgan s law to invert it and find the expression for the output Karnaugh Map A complicated logic expression can be simplified using Boolean algebra However it may not lead to the simplest form of a logic expression A systematic method for minimization of a logic expression is Karnaugh map which is a graphical approach It is an array of squares Each square represents a row in the truth table In karnaugh map in each pair of adjacent squares only one variable is different Finding minimum SOP Create a K map from the desired output Look for the least number of groups of 2 4 or 8 that covers the 1 s Try to find the largest group Find the minimum SOP by the logical sum of the expression of each goup Finding minimum POS Create a K map with the inverted output replace output of 1 by 0 and vice versa Look for the least number of goups of 2 4 or 8 that covers the 1 s Try to find the largest group Find the minimum SOP by the logical sum of the expression of each goup Use DeMorgan s law to convert SOP to POS BCD to 7 segment display The 7 segment display is used to display numbers 0 to 9 using 7 independent LEDs The input is in BCD Binary Coded Decimal and the output is the display of the equivalent input decimal number For example if the input is 0011 3 the segments A B C D and G are on to display 3 Find the logic expression for control of segment A

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