Digital Electronics: Principles, Devices and Applications

Boolean Algebra and Simplification Techniques 231The simplified version of this Boolean expression is given by BE + BDE + BDE. Determine ifthere are any ‘don’t care’ entries. If yes, find them.Yes, ABCDE ABCDE ABCDE5. Write minterm and maxterm Boolean functions expressed by fA B C = 0, 3, 7minterm: ABC + ABC + ABC + ABC + ABCmaxterm:A + B + CA + B + CA + B + C6. Write a simplified maxterm Boolean expression for 0, 4, 5, 6, 7, 10, 14 using the Karnaughmapping method.A + BA + B + C + DA + C + D7. Simplify the following Boolean functions using the Quine–McCluskey tabulation method:(a) f(A, B, C, D, E, F, G) = (20, 21, 28, 29, 52, 53, 60, 61);(b) f(A, B, C, D, E, F) = (6, 9, 13,18,19, 25, 26, 27, 29, 41, 45, 57, 61).(a ACEF; (b CEF + ABDE + ABCDEF8. (a) Simplify the Boolean function fX Y Z = YZ + XZ for the ‘don’t care’ condition expressedas XY + XYZ + XYZ.(b) Simplify the Boolean function given by fA B C = A + B + CA + B + CA + B + C forthe don’t care condition expressed as A + BA + B + C.(a) 1; (b) ACFurther Reading1. Holdsworth, B. and Woods, C. (2002) Digital Logic Design, Newnes, Oxford, UK.2. Chen, W.-K. (2003) Logic Design, CRC Press, FL, USA.3. Floyd, T. L. (2005) Digital Fundamentals, Prentice-Hall Inc., USA.4. Tokheim, R. L. (1994) Schaum’s Outline Series of Digital Principles, McGraw-Hill Companies Inc., USA.