Boolean Algebra and Simplification Techniques
231
The simplified version of this Boolean expression is given by BBE + BBDDE + BBDDE. Determine if
there are any ‘don’t care’ entries. If yes, find them.
Yes, AABBCCDDEE AABBCCDDEE AABBCCDDE
5. Write minterm and maxterm Boolean functions expressed by ffAA BB CC = 0, 3, 7
minterm: AABBC + AABBC + AABBC + AABBC + AABBC
maxterm:A + B + CCCCA + B + CCCCA + B + CC
6. Write a simplified maxterm Boolean expression for 0, 4, 5, 6, 7, 10, 14 using the Karnaugh
mapping method.
A + BBBBA + B + C + DDDDA + C + DD
7. 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).
(aa AACCEEF ; (bb CCEEF + AABBDDE + AABBCCDDEEF
8. (a) Simplify the Boolean function ffXX YY ZZ = YYZ + XXZ for the ‘don’t care’ condition expressed
as XXY + XXYYZ + XXY YZ.
(b) Simplify the Boolean function given by ffAA BB CC = A + B + CCCCA + B + CCCCA + B + CC for
the don’t care condition expressed as A + BBBBA + B + CC.
(a) 1; (b) AAC
Further Reading
1. 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.