7485 magnitude comparator — determine outputs from given inputs and cascade (expansion) signals Given a 7485 4-bit magnitude comparator with the following values: A0 = 0, B0 = 1, (IA < B) = 0; A1 = 1, B1 = 0, (IA = B) = 1; A2 = 1, B2 = 0, (IA > B) = 0; A3 = 0, B3 = 0. What are the states of the three outputs A = B, A < B, and A > B?

Difficulty: Medium

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

Explanation:


Introduction / Context:
The 7485 is a 4-bit magnitude comparator providing three primary outputs: A > B, A = B, and A < B. It also includes cascade (expansion) inputs to chain devices for wider word lengths. Correctly interpreting bit significance and the expansion inputs is essential to determine the final comparison result.


Given Data / Assumptions:

  • A3..A0 and B3..B0 represent 4-bit words with A3/B3 as the most significant bits.
  • Expansion inputs are: (IA < B), (IA = B), (IA > B) = 0, 1, 0 respectively, meaning higher-order sections are equal.
  • Bit values provided: A3 = 0, B3 = 0; A2 = 1, B2 = 0; A1 = 1, B1 = 0; A0 = 0, B0 = 1.


Concept / Approach:
When the expansion input IA = B = 1, the present 4-bit section decides the result. Evaluate from MSB to LSB: the first bit position where A and B differ determines the outcome. If they are equal through all bits, output A = B = 1; otherwise assert A > B or A < B at the first differing position with A or B larger.


Step-by-Step Solution:

Compare MSB (A3 vs B3): 0 vs 0 → equal so continue.Next bit (A2 vs B2): 1 vs 0 → A is greater here; decision made.Lower bits do not change the outcome once a higher bit decides the comparison.Therefore: A > B = 1, A < B = 0, A = B = 0.


Verification / Alternative check:
Interpreting A and B as unsigned: A = 0b0110x (given lower bits) is larger than B since A2 = 1 and B2 = 0 at the first differing position. This aligns with the standard priority of higher-order bits in magnitude comparison.


Why Other Options Are Wrong:

  • Any option asserting A < B contradicts the MSB-first comparison (A2 > B2).
  • Asserting A = B is impossible because multiple bits differ.
  • All zeros or all ones outputs cannot occur for valid comparisons with IA = B = 1.


Common Pitfalls:

  • Reading bits LSB-to-MSB; must evaluate MSB-first.
  • Ignoring expansion inputs; IA = B must be 1 to let this stage decide.


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

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