门| Sudo GATE 2021 测验 |问题 25

Introduction

This is a solution for problem 25 of the Sudo GATE 2021 quiz on Gates. The problem statement is as follows:

A circuit has three inputs A, B and C and one output F, which is 1 if the inputs are in the sequence A-B-C or A-B- (C complement). Otherwise, the output is 0. Which gate structure can be used to implement this circuit?

In this solution, we will look at how we can use a combination of AND, OR, NOT, and XOR gates to implement the required circuit.

Solution

To implement the circuit, we need to check for two sequences: A-B-C and A-B-(C complement). First, let's consider the A-B-C sequence. We can use three AND gates to check if the inputs are A, B, and C, respectively. We can then use an OR gate to combine these outputs. The resulting circuit would look like this:

         +-----+     +-----+     +-----+
 A o-----| AND |-----| AND |-----|     |
         +-----+     +-----+     | OR  |----- F
 B o-----| AND |-----|     |-----|     |
         +-----+     |     |     |     |
 C o-----| AND |-----|     |     +-----+
         +-----+     +-----+

Now let's consider the A-B-(C complement) sequence. We can use a NOT gate to invert the C input, and then use an XOR gate to check if the inputs are A, B, and NOT C, respectively. We can then use another OR gate to combine these outputs. The resulting circuit would look like this:

         +-----+     +-----+     +-----+     +-----+
 A o-----| XOR |-----| XOR |-----|     |-----| OR  |----- F
         +-----+     +-----+     |     |     |     |
 B o-----| XOR |-----|     |-----| NOT |-----|     |
         +-----+     | NOT |     | AND |     |     |
 C o-----| NOT |-----| AND |-----|     |     +-----+
         +-----+     +-----+     +-----+

Conclusion

In this solution, we have seen how we can use a combination of AND, OR, NOT, and XOR gates to implement a circuit that checks for the input sequences A-B-C and A-B-(C complement). We have also provided the circuit diagrams for these implementations in markdown format.