Explanation:

The carry generation function is a key component in the design of adders, which are used to perform addition operations in digital circuits. The carry generation function determines whether there is a carry generated when adding two bits. In the given expression, ci represents the carry input, xi represents the input bit, and yi represents the output bit.

Carry Generation Function:
The carry generation function is given by the expression:
ci+1 = yi * ci + xi * yi

This function calculates the carry generated in the addition of two bits, xi and yi, with a carry input ci. It considers both the input bits and the carry input to determine the carry output.

Implementation in Full Adders:
Full adders are combinational circuits that can add three input bits (two data bits and a carry input) and generate a sum bit and a carry output. The carry generation function is implemented in full adders to generate the carry output.

In a full adder, the carry generation function is realized by using AND and OR gates. The input bits xi and yi are connected to the AND gate, which generates the carry when both input bits are set to 1. The carry input ci is connected to the AND gate as well. The output of the AND gate and the input bits xi and yi are connected to the OR gate, which combines the carry generated by the AND gate and the carry input.

By implementing the carry generation function in full adders, the carry output is generated based on the input bits and the carry input. This allows for the addition of multiple bits by cascading multiple full adders together.

Conclusion:
The carry generation function is implemented in full adders to generate the carry output in addition operations. Full adders use AND and OR gates to realize the carry generation function based on the input bits and the carry input. This implementation allows for the addition of multiple bits in digital circuits.