sol4 - Solutions of Assignment 4 Question 1 (X+Y) •...

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Unformatted text preview: Solutions of Assignment 4 Question 1 (X+Y) • (X’+Z) = X • (X’+Z) +Y • (X’+Z) = X • X’ + X • Z + Y • X’ + Y • Z = 0 + X • Z + Y • X’ + Y • Z = X • Z + X’ • Y Question 2 Row 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Question 3 (T8) (T8) (T5) (T11) W 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 X 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 Y 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 Z 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 F 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 CD Canonical sum of products : AB F=X’•Y’•Z’+X•Y’•Z’+X•Y’•Z+X•Y•Z’+X•Y•Z Canonical product of sums: 00 F=(X+Y+Z’) • (X+Y’+Z) • (X+Y’+Z’) Question 4 A minimal sum-of-products: F=B’• D’+B’• C+A’•C • D’+A•C’•D Question 5 00 1 01 0 11 1 10 1 01 0 0 0 1 11 0 1 0 0 10 A minimal product-of-sums: F= (B’+C+D) • (A+C+D’) • (A’+B’+C’) • (B’+C’+D’) 1 1 1 1 Question 6 A minimal sum-of-products: F=C’ • D+A’ • B CD 00 AB 00 0 01 1 11 0 10 0 01 Question 7 A minimal product-of-sums: F=(C+D) • (A’+C’) • (B+C’) x 0 1 1 1 11 1 x 0 10 Question 8 Yes. 1. (X•X)’=X’ 2. [(X•X)’ •(Y•Y)’]’=X+Y 3. [(X•Y)’ •(X•Y)’]’=X•Y Obviously, NAND Gates form a complete set. 0 1 0 0 (Inverter) (OR Gate) (AND Gate) ...
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sol4 - Solutions of Assignment 4 Question 1 (X+Y) •...

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