Design a combinational circuit with three inputs x, y and z and three outputs A, B and C. When
x = 0, y = 0, z = 0, the outputs A, B and C should be 0.
The truth table for the circuit is as follows:
x | y | z || A | B | C
--|---|--||---|---|---
0 | 0 | 0 || 0 | 0 | 0
0 | 0 | 1 || 0 | 0 | 1
0 | 1 | 0 || 0 | 1 | 0
0 | 1 | 1 || 0 | 1 | 1
1 | 0 | 0 || 1 | 0 | 0
1 | 0 | 1 || 1 | 0 | 1
1 | 1 | 0 || 1 | 1 | 0
1 | 1 | 1 || 1 | 1 | 1
Based on the truth table, we can derive the following logic expressions for the outputs:
A = x OR y OR z
B = NOT(x) AND y AND z
C = x XOR y XOR z
Thus, the combinational circuit can be implemented as follows:
Note that the circuit consists of three basic logic gates - OR gate, AND gate and XOR gate - connected in the specified configuration.
To design a combinational circuit with three inputs x, y, and z, and three outputs A, B, and C that meets the given conditions, follow these steps:
Step 1: Construct a truth table
To design a combinational circuit, we need to create a truth table that maps the inputs (x, y, z) to the corresponding outputs (A, B, C) based on the given condition.
x y z | A B C
--------------------------
0 0 0 | 0 0 0
0 0 1 | 0 0 1
0 1 0 | 0 1 0
0 1 1 | 0 0 1
1 0 0 | 1 1 0
1 0 1 | 1 0 0
1 1 0 | 1 1 0
1 1 1 | 1 1 1
Step 2: Identify the logical expressions for each output
Looking at the truth table, we can derive logical expressions for each output based on the given conditions.
A = x OR y
B = (x AND y) OR (x AND z)
C = z
Step 3: Implement the logical expressions using logic gates
Based on the logical expressions, we can implement the combinational circuit using logic gates. Here's a possible circuit implementation:
```
____
x --| OR |-| |
y --| | | OR|-- A
z --|_________| |____|
x --| AND |
y --| ____| ____
z --| | OR | | |
| | | | OR|-- B
|___|_____|___|____|
____
x --| AND |-| |
y --| | | AND|-- C
z --|__________| |____|
```
In this circuit, the OR gate is used to implement the logical expressions for A and B, while the AND gate is used to implement the logical expression for C. The OR gate takes the inputs x, y, and z to compute the output A, while the AND gate combines inputs x and y, and inputs x and z, and then passes them through another OR gate to compute the output B. The third AND gate takes the input z to compute the output C.
That's it! You've designed a combinational circuit with three inputs (x, y, z) and three outputs (A, B, C), based on the given conditions.