Design a combinational circuit that can detect whether the 3-bit input binary number is even,odd, or prime number.(a) Find the number of inputs, and outputs.(b) Draw the truth table for the design problem(c) Implement the circuit using 3 × 8 Decoder.(d) Explain the design implementation in your own words. Lack of understanding of theproblem, and incorrect explanation will lead to 0 in the question.
Question
Design a combinational circuit that can detect whether the 3-bit input binary number is even,odd, or prime number.(a) Find the number of inputs, and outputs.(b) Draw the truth table for the design problem(c) Implement the circuit using 3 × 8 Decoder.(d) Explain the design implementation in your own words. Lack of understanding of theproblem, and incorrect explanation will lead to 0 in the question.
Solution
(a) Number of Inputs and Outputs: The number of inputs is 3 because we are dealing with a 3-bit binary number. The number of outputs is 3 because we are detecting whether the number is even, odd, or prime.
(b) Truth Table: The truth table for a 3-bit binary number is as follows:
| Binary | Decimal | Even | Odd | Prime |
|---|---|---|---|---|
| 000 | 0 | 1 | 0 | 0 |
| 001 | 1 | 0 | 1 | 1 |
| 010 | 2 | 1 | 0 | 1 |
| 011 | 3 | 0 | 1 | 1 |
| 100 | 4 | 1 | 0 | 0 |
| 101 | 5 | 0 | 1 | 1 |
| 110 | 6 | 1 | 0 | 0 |
| 111 | 7 | 0 | 1 | 1 |
(c) Circuit Implementation using 3x8 Decoder: The 3x8 decoder will have 3 inputs (representing the 3-bit binary number) and 8 outputs. Each output represents one of the 8 possible 3-bit binary numbers. We can connect the outputs of the decoder to the inputs of three OR gates. The first OR gate will have inputs from the outputs of the decoder that represent even numbers (000, 010, 100, 110). The second OR gate will have inputs from the outputs of the decoder that represent odd numbers (001, 011, 101, 111). The third OR gate will have inputs from the outputs of the decoder that represent prime numbers (001, 010, 011, 101, 111).
(d) Design Implementation Explanation: The design works by decoding the 3-bit binary input into one of 8 possible outputs. These outputs are then fed into three OR gates. The first OR gate checks if the number is even, the second checks if the number is odd, and the third checks if the number is prime. If the output of an OR gate is 1, then the input number satisfies that condition (even, odd, or prime). If the output is 0, then the input number does not satisfy that condition.
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