Magnitude comparison — determine comparator outputs for A and B. Given A = 1100₂ and B = 1001₂ applied to a 3-output magnitude comparator, what are the output levels for A > B, A < B, and A = B?

Introduction / Context:
Digital magnitude comparators (such as the 7485 family) produce three outputs that indicate whether one binary word is greater than, less than, or equal to another. Interpreting these outputs is a basic skill for designing decision logic, sorting networks, and address decoding hardware.

Given Data / Assumptions:

• A = 1100₂ (binary).
• B = 1001₂ (binary).
• Outputs are independent indicator lines for A > B, A < B, A = B (active-HIGH).

Concept / Approach:
Convert each binary number to decimal or compare bit-by-bit from MSB to LSB. The first differing bit from the left determines the result: if A’s bit is 1 and B’s is 0, then A > B; if opposite, A < B; if all bits equal, A = B.

Step-by-Step Solution:

Verification / Alternative check:
Bitwise MSB-first: compare bits at positions 2^3, 2^2, 2^1, 2^0. At 2^2 (the second bit), A has 1 while B has 0, and no higher bits differ; therefore A > B without needing to check lower bits.

Why Other Options Are Wrong:

• Any option asserting A < B is false because A (12) clearly exceeds B (9).
• Any option asserting A = B is false because they differ at multiple bit positions.

Common Pitfalls:

• Mistaking LSB for MSB during comparison.
• Adding bits incorrectly (e.g., miscounting the 4’s or 1’s places).

Final Answer:
A > B = 1, A < B = 0, A = B = 0