Final answer:
A 1-bit comparator can be designed using basic logic gates: an AND gate combined with a NOT gate for the A>B output, and an XNOR gate for the A=B output. This simple gate-level configuration allows for efficient comparison of two single-bit inputs.
Step-by-step explanation:
To design a comparator that compares two 1-bit inputs at the gate level, we need to produce two outputs: one that indicates if input A is greater than input B (A>B), and another that indicates if input A and input B are equal (A=B). The truth table for such a comparator is simple, with four possible input combinations for the two 1-bit inputs (A and B).
- If both inputs are equal (A=B), the A>B output is 0 and the A=B output is 1.
- If A is 1 and B is 0, then A>B is 1 and A=B is 0.
- If A is 0 and B is 1, then A>B is 0 and A=B is 0.
- If both inputs are 0, A is not greater than B, so A>B is 0 and A=B is 1.
Based on this, you can construct the comparator using basic logic gates. The A>B output can be directly derived from an AND gate, where A is directly connected to one input of the AND gate, and B is connected to another input through a NOT gate. This configuration will only produce a high output when A is high and B is low.
The A=B output can be derived using an XNOR gate since the output of an XNOR gate is high only when both inputs are the same. Hence, by directly connecting both A and B inputs to an XNOR gate, we achieve the desired A=B comparison output.
Overall, the smallest 1-bit comparator can be designed with just one AND gate and one XNOR gate, reflecting the simplicity of comparing two single-bit inputs.