Question 7 on digital from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper.

## Q7. The output Y of a 2-bit comparator is logic 1 whenever the 2 bit input A is greater than 2 bit input B. The number of combinations for which output is logic 1 is

## (A) 4

## (B) 6

## (C) 8

## (D) 10

## Solution

Let’s write all the 16 possible combinations of A and B and count the number of times A is greater than B. Can easily see that the count is 16.

A |
B |
Out |

0 | 0 | 0 |

0 | 1 | 0 |

0 | 2 | 0 |

0 | 3 | 0 |

1 | 0 | 1 |

1 | 1 | 0 |

1 | 2 | 0 |

1 | 3 | 0 |

2 | 0 | 1 |

2 | 1 | 1 |

2 | 2 | 0 |

2 | 3 | 0 |

3 | 0 | 1 |

3 | 1 | 1 |

3 | 2 | 1 |

3 | 3 | 0 |

TOTAL |
6 |

Alternately, pick each value of A and count the number of instances when A is greater than B. The count is 0 + 1 + 2 + 3 for A = 0,1,2,3 respectively.

**Based on the above, the right choice is (B) 6**

** **

## References

[1] GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf