Design a combinational circuit with three inputs x, y and z and three outputs A, B and C. When
the binary input is 0, 1, 2 or 3, the binary output is two greater than the input. When the binary
input is 4, 5, 6 or 7, the binary output is three lesser the input.
To design a combinational circuit that meets the given specifications, you can use a combination of logic gates. Here's one possible solution:
Inputs: x, y, z
Outputs: A, B, C
1. Set up a decoder with three inputs (x, y, z) and eight outputs (D0, D1, D2, D3, D4, D5, D6, D7). The decoder will convert the binary input to its corresponding output.
2. Connect the decoder outputs (D0, D1, D2, D3, D4, D5, D6, D7) to an 8-input OR gate. This will create a combined input signal that detects any of the values 0 to 7.
3. Use a 3-bit binary encoder to convert the combined input signal from step 2 into a 3-bit binary output (E0, E1, E2), which represents the input value.
4. Apply an adder circuit to add 2 (binary 0010) to the encoder outputs when the binary input is 0, 1, 2, or 3. Connect the output of the adder to the outputs A, B, and C.
5. Apply a subtractor circuit to subtract 3 (binary 0011) from the encoder outputs when the binary input is 4, 5, 6, or 7. Connect the output of the subtractor to the outputs A, B, and C.
By following these steps, the combinational circuit will produce the desired outputs based on the given inputs.
To design a combinational circuit that meets the given specifications, follow these steps:
Step 1: Create a truth table with inputs x, y, and z, and outputs A, B, and C.
```
| x | y | z | A | B | C |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 2 | 2 | 2 |
| 0 | 1 | 1 | 3 | 3 | 3 |
| 1 | 0 | 0 | 2 | 2 | 2 |
| 1 | 0 | 1 | 3 | 3 | 3 |
| 1 | 1 | 0 | 4 | 4 | 4 |
| 1 | 1 | 1 | 5 | 5 | 5 |
```
Step 2: Write the Boolean expressions for outputs A, B, and C based on the truth table.
```
A = x + y + z
B = x + y + z
C = x + y + z
```
Step 3: Simplify the Boolean expressions if possible. In this case, the expressions are already simplified.
Step 4: Implement the simplified Boolean expressions using logic gates.
- For A, B, and C, use OR gates to combine the inputs x, y, and z.
```
A = x OR y OR z
B = x OR y OR z
C = x OR y OR z
```
Step 5: Draw the circuit diagram based on the logic gate implementation.
```
_______
x ----| |
| OR |----- A
y ----| |
| |
z ----|_______|
_______
x ----| |
| OR |----- B
y ----| |
| |
z ----|_______|
_______
x ----| |
| OR |----- C
y ----| |
| |
z ----|_______|
```
That's it! You have designed a combinational circuit that satisfies the given conditions with three inputs (x, y, and z) and three outputs (A, B, and C).