For a Boolean function of n variables, we can index a min-term (c.g., X XX3X) by...

 

 

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For a Boolean function of n variables, we can index a min-term (c.g., X₁ X₂X3X₁) by m, (i = 0, 1,..., 2"-1) and we can determine the index i as follows: we construct a binary number of n bits by putting a 1 corresponding to the positions of a direct term and a 0 corresponding to a complemented term (X₁X₂X3X₁ → (1000)2) then we convert this binary number to the decimal number i=8 ((1000)28). Consider the following function: F = f(A, B, C, D)= mo + m + m₂ + ma + ms+ms + M15 (1) a) Construct the truth table. (4 points) b) Write the function in SOP and POS form. (5 points) c) Using K-Map to simplify the function and write the simplified function. (6 points) d) Draw the circuit according to the function you wrote in c) only use AND, OR, NOT gates. (5 points) e) Consider the function: G = g(A, B, C, D) = A + AB+ AD+B+BD+BCD (2) Simplify the function (using logic properties or the K-map) to the most simplified form and draw the circuit with only NAND gates. (10 points) Hint: DeMorgan's Theorem XY=X+Y. For a Boolean function of n variables, we can index a min-term (c.g., X₁ X₂X3X₁) by m, (i = 0, 1,..., 2"-1) and we can determine the index i as follows: we construct a binary number of n bits by putting a 1 corresponding to the positions of a direct term and a 0 corresponding to a complemented term (X₁X₂X3X₁ → (1000)2) then we convert this binary number to the decimal number i=8 ((1000)28). Consider the following function: F = f(A, B, C, D)= mo + m + m₂ + ma + ms+ms + M15 (1) a) Construct the truth table. (4 points) b) Write the function in SOP and POS form. (5 points) c) Using K-Map to simplify the function and write the simplified function. (6 points) d) Draw the circuit according to the function you wrote in c) only use AND, OR, NOT gates. (5 points) e) Consider the function: G = g(A, B, C, D) = A + AB+ AD+B+BD+BCD (2) Simplify the function (using logic properties or the K-map) to the most simplified form and draw the circuit with only NAND gates. (10 points) Hint: DeMorgan's Theorem XY=X+Y.

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a To construct the truth table for the given function F fA B C D m0 m1 m2 m3 m5 m18 m15 we need to evaluate the function for all possible combinations ... View the full answer