Implementing Logic Function F = ABC + DE with AND/NOT Gates
The given logic function is $F = ABC + DE$. We need to implement this using only 2-input AND gates and NOT gates, determining the minimum number required.
Breaking Down the Function
The function consists of two product terms, $ABC$ and $DE$, combined by an OR operation ('+').
- Term 1 ($ABC$): Requires implementation using 2-input AND gates. This is done by cascading two 2-input AND gates:
- Gate 1: $A \text{ AND } B$
- Gate 2: (Output of Gate 1) $\text{ AND } C$
- Term 2 ($DE$): Requires one 2-input AND gate:
- Gate 3: $D \text{ AND } E$
- OR Operation ($Term1 + Term2$): Since only AND and NOT gates are allowed, the OR operation must be synthesized. Using De Morgan's theorem, the OR operation $X + Y$ can be expressed as $\text{NOT}( (\text{NOT } X) \text{ AND } (\text{NOT } Y) )$.
- First NOT: Invert the output of Term 1 ($ABC$). (1 NOT gate)
- Second NOT: Invert the output of Term 2 ($DE$). (1 NOT gate)
- AND Operation: Combine the outputs of the two NOT gates using a 2-input AND gate. (1 AND gate)
- Final NOT: Invert the output of the AND gate to get the final OR result. (1 NOT gate)
Calculating Total Gate Count
Summing the gates required for each part:
- Total AND gates: 2 (for $ABC$) + 1 (for $DE$) + 1 (for OR synthesis) = 4 AND gates.
- Total NOT gates: 1 (for NOT Term 1) + 1 (for NOT Term 2) + 1 (for final NOT) = 3 NOT gates.
Therefore, the minimum number of gates required is 4 two-input AND gates and 3 NOT gates.
Important Questions from Logic Gates
A two-input logic gate is giving high output only when both the inputs are high. For all other input conditions, the output is low. Select the correct logic gate.
The output is high only if one of the input is high. The above statement represents _____
The number of gate inputs, required to realize expression ABC + AB̅CD + EF̅ + AD is
Which of the following is logically equivalent?
A. ¬p → (q → r) and q → (p ∨ r)
B. (p → q) → r and p → (q → r)
C. (p → q) → (r → s) and (p → r) → (q → s)
Choose the correct answer from the options given below :
Consider the expression Y = P ⨁ Q ⨁ R where P, Q, R are the input variables and Y is the output variable. Y will be logic 0 if
(A) an odd number of input variables are 1
(B) an even number of input variables are 1
(C) an odd number of inputs variables are 0
(D) an even number of input variable are 0
(E) an odd number of input variable between 0 and 1
Choose the correct answer from the options given below:
