ECEN 215, Principles of Electrical EngineeringDr. Mina RahimianLecture# 25 Date: 11/25/13Finding logic expression from the truth tableThere 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 MapA 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 SOPCreate 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 POSCreate 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 displayThe 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
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