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lecture3

# lecture3 - Two-level Combinational Circuit Z Jerry Shi...

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1 Two-level Combinational Circuit Z. Jerry Shi Department of Computer Science and Engineering University of Connecticut CSE2300W:Digital Logic Design Brute-force design Truth table Æ Canonical sum (Sum of minterms) Example: Design a circuit to detect prime numbers between 0-15 Given a 4-bit input, N 3 N 2 N 1 N 0 , produce a 1 output for N = 1, 2, 3, 5, 7, 11, 13 and a 0 otherwise row N 3 N 2 N 1 N 0 F 0 0 0 0 0 0 1 0 0 0 1 1 2 0 0 1 0 1 3 0 0 1 1 1 4 0 1 0 0 0 5 0 1 0 1 1 6 0 1 1 0 0 7 0 1 1 1 1 8 1 0 0 0 0 9 1 0 0 1 0 10 1 0 1 0 0 11 0 0 1 1 1 12 1 1 0 0 0 13 1 1 0 1 1 14 1 1 1 0 0 15 1 1 1 1 0 F = Σ N3, N2, N1, N0 (1,2,3,5,7,11,13)

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2 Minterm list Æ Canonical sum Algebraic simplification Theorem T10: X • Y + X • Y ' = X Reduce number of gates and gate inputs