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The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is
  • a)
    4
  • b)
    6
  • c)
    8
  • d)
    10
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input...
The only possible combinations are
A = 01 and B = 0 0
A = 10 and B = 00, 01
A = 11 and B = 00, 01, 10
So there are only 6 combinations
Tips and Tricks:

where n = 2 bit
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Community Answer
The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input...
Understanding the 2-Bit Comparator
A 2-bit comparator compares two 2-bit binary numbers, A and B. The output Y is set to logic 1 when A is greater than B.
2-Bit Input Combinations
- Each 2-bit number can take values from 00 to 11, which translates to decimal values from 0 to 3.
- The possible combinations of A and B can be represented as follows:
- A = 00, 01, 10, 11 (4 possibilities)
- B = 00, 01, 10, 11 (4 possibilities)
- Therefore, the total combinations of A and B are 4 x 4 = 16.
Conditions for Y = 1
Now, we need to determine when A > B in these combinations:
1. A = 00: A is never greater than B.
2. A = 01:
- A > B when B = 00 (1 combination)
3. A = 10:
- A > B when B = 00 or 01 (2 combinations)
4. A = 11:
- A > B when B = 00, 01, or 10 (3 combinations)
Counting the Combinations
- From the above, we can count the combinations where A > B:
- For A = 01: 1 combination
- For A = 10: 2 combinations
- For A = 11: 3 combinations
- Total combinations for which Y = 1:
- 1 (from A=01) + 2 (from A=10) + 3 (from A=11) = 6 combinations
Conclusion
Thus, the output Y is logic 1 for a total of 6 combinations, confirming that option 'B' is correct.
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The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, isa)4b)6c)8d)10Correct answer is option 'B'. Can you explain this answer?
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