Introduction / Context:
Multi-bit magnitude comparison often uses cascaded comparators. Standard 4-bit comparator ICs (e.g., 74x85) provide “cascade” inputs (AB) and corresponding outputs so multiple units can be chained to handle wider operands. Correct wiring ensures that the decision made by lower-order bits properly influences the overall result once the upper bits are evaluated.
Given Data / Assumptions:
- Two 4-bit comparators are used to compare 8-bit numbers A7..A0 and B7..B0.
- The least significant comparator evaluates A3..A0 vs. B3..B0.
- The most significant comparator evaluates A7..A4 vs. B7..B4.
Concept / Approach:
The cascade mechanism propagates the relationship found in lower bits to the higher-stage decision. The lower (LSB) comparator produces the intermediate AB outputs. These must feed the corresponding cascade inputs of the upper (MSB) comparator so the final outputs reflect the entire 8-bit comparison, not just the upper nibble independently.
Step-by-Step Solution:
Evaluate low nibble (LSB comparator): obtain signals LT_L, EQ_L, GT_L.Feed these to MSB cascade inputs: LT_in = LT_L, EQ_in = EQ_L, GT_in = GT_L.The MSB comparator uses its own nibble and the cascade inputs to produce final LT, EQ, GT for the full 8-bit numbers.Confirm polarity and pin names per datasheet (some families use active-low signals).
Verification / Alternative check:
Test boundary cases: when upper nibbles are equal, the MSB comparator defers to the cascaded equality from the LSB stage; when upper nibbles differ, MSB outputs dominate regardless of LSB state.
Why Other Options Are Wrong:
Tying to LSB inputs or ground ignores the lower nibble result, breaking correctness.Forcing A=B HIGH and others LOW defeats dynamic comparison and yields wrong outputs if MSB nibbles differ.
Common Pitfalls:
Mixing up active-high/active-low cascade pins; always check the exact device logic levels.Failing to route EQ correctly, which is crucial when upper nibbles match.
Final Answer:
Connect them to the cascade outputs from the least significant 4-bit comparator
Discussion & Comments