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Section generate, create none none on none projects barcode References 4.2 4.3 4.

4 4.5. 4.10 Write none for none the canonical sum and product for each of the following logic functions: (a) F = X,Y,Z(0,3) (b) F = A,B,C(1,2,4) (c) F = A,B,C,D(1,2,5,6) (d) F = M,N,P(0,1,3,6,7) (f) F = A B + B C + A. 4.11 If the canonical sum for an n-input logic function is also a minimal sum, how many literals are in each product term of the sum Might there be any other minimal sums in this case 4.12 Give two reasons why the cost of inverters is not included in the definition of minimal for logic minimization.

. DO NOT COPY none none DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY. Prove theor ems T2 T5 using perfect induction. Prove theorems T1 T3 and T5 using perfect induction. Prove theorems T6 T9 using perfect induction.

According to DeMorgan s theorem, the complement of X + Y Z is X Y + Z . Yet both functions are 1 for XYZ = 110. How can both a function and its complement be 1 for the same input combination What s wrong here Use the theorems of switching algebra to simplify each of the following logic functions: (b) F = A B + A B C D + A B D E + A B C E + C D E (c) F = M N O + Q P N + P R M + Q O M P + M R (a) F = W X Y Z (W X Y Z + W X Y Z + W X Y Z + W X Y Z) Write the truth table for each of the following logic functions:.

(a) F = X Y + X Y Z (b) F = W X + Y Z + X Z (c) F = W + X (Y + Z). (d) F = A B + B C + C D + D A (h) F = (((A + B) + C ) + D) . (e) F = V W + X Y Z (f) F = (A + B + C D) (B + C + D E ). (g) F = (W X) (Y + Z ) . (i) F = (A + B + C) (A + B + D ) (B + C + D ) (A + B + C + D). Write the t none none ruth table for each of the following logic functions: (a) F = X Y Z + X Y Z + X Y Z (c) F = A B + A B C + A B C. (b) F = M N + M P + N P (d) F = A B (C B A + B C ) (h) F = X Y + Y Z + Z X (e) F = X Y (X Y Z + X Y Z + X Y Z + X Y Z) (f) F = M N + M N P (g) F = (A + A ) B + B A C + C (A + B ) (A + B). Write the c none for none anonical sum and product for each of the following logic functions: (b) F = A,B(0,1,2) (d) F = W,X,Y(0,1,3,4,5) (f) F = V + (W X) . (a) F = X,Y(1,2). (c) F = A,B,C(2,4,6,7) (e) F = X + Y Z (e) F = X + Y Z + Y Z Copyright 1999 by John F. Wakerly Copying Prohibited 4 . Combinational Logic Design Principles DO NOT COPY none none DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY. (a) F = X, Y,Z(1,3,5,6,7) (b) F = W,X,Y,Z(1,4,5,6,7,9,14,15) (c) F = W,X,Y(0,1,3,4,5) (d) F = W,X,Y,Z(0,2,5,7,8,10,13,15) (e) F = A,B,C,D(1,7,9,13,15) (f) F = A,B,C,D(1,4,5,7,12,14,15) (a) F = A,B,C(0,1,2,4) (b) F = W,X,Y,Z(1,4,5,6,11,12,13,14) (c) F = A,B,C(1,2,6,7) (e) F = W,X,Y,X(1,2,4,7,8,11,13,14) (a) F = W,X,Y,Z(0,1,3,5,14) + d(8,15) (c) F = A,B,C,D(1,5,9,14,15) + d(11) (e) F = W,X,Y,Z(3,5,6,7,13) + d(1,2,4,12,15) (a) F = W X + W Y (c) F = W Y + X Y + W X Z (e) F = (W + X + Y) (X + Z ) (g) F = (W + Y + Z ) (W + X + Y + Z) (X + Y ) (X + Z) Exercises Copyright 1999 by John F. Wakerly. 4.13 Using none none Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions. Indicate the distinguished 1-cells in each map.

. 4.14 Find a minimal product-of-sums expression for each function in Drill 4.13 using the method of Section 4.

3.6. 4.

15 Find a minimal product-of-sums expression for the function in each of the following figures and compare its cost with the previously found minimal sum-ofproducts expression: (a) Figure 4-27; (b) Figure 4-29; (c) Figure 4-33. 4.16 Using Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions.

Indicate the distinguished 1-cells in each map. (d) F = W,X,Y,Z(0,1,2,3,7,8,10,11,15). (f) F = A, none for none B,C,D(1,3,4,5,6,7,9,12,13,14). 4.17 Find a minimal product-of-sums expression for each function in Drill 4.16 using the method of Section 4.

3.6. 4.

18 Find the complete sum for the logic functions in Drill 4.16(d) and (e). 4.

19 Using Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions. Indicate the distinguished 1-cells in each map. (b) F = W,X,Y,Z(0,1,2,8,11) + d(3,9,15) (d) F = A,B,C,D(1,5,6,7,9,13) + d(4,15).

4.20 Repeat none none Drill 4.19, finding a minimal product-of-sums expression for each logic function.

4.21 For each logic function in the two preceding exercises, determine whether the minimal sum-of-products expression equals the minimal product-of-sums expression. Also compare the circuit cost for realizing each of the two expressions.

4.22 For each of the following logic expressions, find all of the static hazards in the corresponding two-level AND-OR or OR-AND circuit, and design a hazard-free circuit that realizes the same logic function. (b) F = W X Y + X Y Z + X Y (d) F = W X + Y Z + W X Y Z + W X Y .

(f) F = (W + Y +Z ) (W + X + Z ) (X +Y+Z).
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