Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates. Please refer to the given truth table for your design
B. Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates. (20 Points)
F = AC’ + B’C
C. Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates. USE MAX TERMS FOR IMPLEMENTATION. (30 Points)
F=A+B’+C
D. Design a 3-input XOR gate using a 3-8 Line decoder and basic gates. USE MAX TERMS FOR IMPLEMENTATION. (35 Points)
The Correct Answer and Explanation is :
Implementation of Function F(A, B, C) Using a 3-to-8 Line Decoder and Basic Gates
(A) Implementing F(A,B,C) using a 3-to-8 Decoder and Basic Gates
A 3-to-8 decoder has three inputs (A, B, C) and eight outputs corresponding to minterms (m0 to m7). It generates an output of 1 for exactly one input combination.
Truth Table for 3-to-8 Decoder Outputs
| A | B | C | Decoder Outputs |
|---|---|---|---|
| 0 | 0 | 0 | m0 = 00000001 |
| 0 | 0 | 1 | m1 = 00000010 |
| 0 | 1 | 0 | m2 = 00000100 |
| 0 | 1 | 1 | m3 = 00001000 |
| 1 | 0 | 0 | m4 = 00010000 |
| 1 | 0 | 1 | m5 = 00100000 |
| 1 | 1 | 0 | m6 = 01000000 |
| 1 | 1 | 1 | m7 = 10000000 |
From the given function:
F = AC’ + B’C
- AC’: It is active for minterms m4 (100) and m6 (110)
- B’C: It is active for minterms m1 (001) and m6 (110)
Thus, F = m1 + m4 + m6
Implementation:
- Use a 3-to-8 decoder to generate minterms.
- Use an OR gate to combine m1, m4, and m6.
(B) Implementing F(A,B,C) using Max Terms
Max term-based implementation:
F = A + B’ + C
From the truth table, we convert it into a Sum of Maxterms:
| A | B | C | F |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
F = (A + B’ + C)
- Implement using basic OR and NOT gates.
(C) Designing a 3-Input XOR Using a 3-to-8 Decoder and Basic Gates
A 3-input XOR function is:
F = A ⊕ B ⊕ C
Truth Table:
| A | B | C | F |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
The function selects minterms m1, m2, m4, m7.
Implementation:
- Use a 3-to-8 decoder to generate the minterms.
- Use an OR gate to combine m1, m2, m4, m7.
Image Representation
Now, I will generate an image showing the circuit implementations using a 3-to-8 line decoder and logic gates.
Here is the generated circuit diagram implementing F(A,B,C) using a 3-to-8 line decoder and basic gates, including the XOR design. Let me know if you need modifications or further clarifications!
