Implement a 4-bit magnitude comparator.

Q.) Implement a 4-bit magnitude comparator.

 Subject: Digital Circuit and System Design

To implement a 4-bit magnitude comparator, we need to compare two 4-bit binary numbers and determine whether one is greater than, less than, or equal to the other. The two 4-bit numbers can be denoted as A and B, with A3 A2 A1 A0 and B3 B2 B1 B0 representing the bits from the most significant bit (MSB) to the least significant bit (LSB).

The 4-bit magnitude comparator will have three outputs:

  1. A > B (A is greater than B)
  2. A < B (A is less than B)
  3. A = B (A is equal to B)

Let's implement the 4-bit magnitude comparator step by step:

Step 1: Define the Inputs and Outputs

Inputs:

  • A3, A2, A1, A0 (4 bits of number A)
  • B3, B2, B1, B0 (4 bits of number B)

Outputs:

  • A>B (A is greater than B)
  • A B, regardless of the other bits.
  • If the MSB of A is less than the MSB of B, then A < B, regardless of the other bits.
  • If the MSBs are equal, we compare the next significant bit, and so on.

For simplicity, let's consider a partial truth table that shows the comparison logic:

| A3 | A2 | A1 | A0 | B3 | B2 | B1 | B0 | A>B | AB = (A3 & ~B3) | (A2 & ~B2 & ~(A3 ^ B3)) | (A1 & ~B1 & ~(A3 ^ B3) & ~(A2 ^ B2)) | (A0 & ~B0 & ~(A3 ^ B3) & ~(A2 ^ B2) & ~(A1 ^ B1))

A B should be true.

  • If A = 0100 and B = 0100, then A = B should be true.
  • If A = 0011 and B = 1100, then A < B should be true.

Example Implementation

Here's an example of how the logic equations can be implemented using logic gates:

A&gt;B = (A3 AND NOT B3) OR
      (A2 AND NOT B2 AND NOT (A3 XOR B3)) OR
      (A1 AND NOT B1 AND NOT (A3 XOR B3) AND NOT (A2 XOR B2)) OR
      (A0 AND NOT B0 AND NOT (A3 XOR B3) AND NOT (A2 XOR B2) AND NOT (A1 XOR B1))

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