Submit in 6 hours: 1. Implement the function F (A, B, C) = A(B+C’D) + BC’ using NAND gates ONLY. 2. Redesign (using Boolean algebra) the following logic circuit in order to make it more efficient. The output X is given as: (See attached)
1. Implementing the function F(A, B, C) = A(B+C’D) + BC’ using NAND gates only involves building a circuit that uses only NAND gates to perform the logical operations required.
To implement this function using NAND gates, we can break it down into smaller steps:
Step 1: Get the complement of D using a NAND gate.
D’ = NAND(D, D)
Step 2: Use a NAND gate to compute B + C’D.
B + C’D = NAND(NAND(B, B), NAND(C’, D’))
Step 3: Use a NAND gate to compute A times (B + C’D).
F1 = NAND(A, B + C’D)
Step 4: Use a NAND gate to compute C’ times B.
F2 = NAND(C’, B)
Step 5: Use a NAND gate to compute F1 + F2.
F(A, B, C) = NAND(F1, F2)
Thus, the function F(A, B, C) = A(B+C’D) + BC’ can be implemented using only NAND gates.
2. Redesigning the given logic circuit to make it more efficient can be achieved by simplifying the Boolean expression and integrating it into a single logic gate implementation.
To begin, let’s simplify the given Boolean expression for X:
X = A’B + AB’C + ABC + A’B’C’
Using Boolean algebra, we can simplify this expression further:
X = A’B + (B + B’)AC + A’B’C’
X = A’B + AC + A’B’C’
Next, we can implement this simplified expression using a minimal set of logic gates. By analyzing the expression, we can observe that it consists of three terms: A’B, AC, and A’B’C’. These terms can be implemented using AND gates and OR gates:
Term 1: A’B can be implemented using an AND gate with inputs A’ and B.
Term 2: AC can be implemented using an AND gate with inputs A and C.
Term 3: A’B’C’ can be implemented using an AND gate with inputs A’, B’, and C’.
Finally, we can combine these three terms using an OR gate to get the output X:
X = (A’B) + (AC) + (A’B’C’)
By redesigning the logic circuit in this way, we have simplified the expression and integrated it into a single logic gate implementation, making it more efficient.
Please note that the above explanations are based on the given information. If there are any additional constraints or specifications, they should be considered for a more accurate design.
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