What is the number of AND gates required in carry circuit for 10- bit look ahead carry adder?Correct answer is '55'. Can you explain this answer?

Question

Answer

Number of AND Gates Required in Carry Circuit for 10-bit Look Ahead Carry Adder

Introduction

A carry adder is a digital circuit that adds two binary numbers and produces the sum as well as the carry. In a 10-bit look ahead carry adder, the carry circuit is designed to generate carry signals for each bit position in advance, based on the inputs and the carry from the previous bit. The number of AND gates required to implement this carry circuit is the subject of this discussion.

Calculation

To calculate the number of AND gates required in the carry circuit for a 10-bit look ahead carry adder, we need to consider the following:

Each bit position requires two AND gates, one for generating the carry and the other for generating the carry propagate signal

The carry propagate signal for a bit position is generated by ANDing the two input bits

The carry signal for a bit position is generated by ANDing the carry propagate signals of the current and previous bit positions

Therefore, the total number of AND gates required in the carry circuit for a 10-bit look ahead carry adder can be calculated as follows:

For the first bit position, only one AND gate is required to generate the carry signal

For the remaining nine bit positions, two AND gates are required for each position

Hence, the total number of AND gates required is: 1 + (2 x 9) = 19

However, we also need to consider the carry lookahead logic, which requires additional AND gates

For the first bit position, no additional AND gates are required

For the remaining nine bit positions, three AND gates are required for each position

Hence, the total number of AND gates required for carry lookahead logic is: 0 + (3 x 9) = 27

Therefore, the total number of AND gates required in the carry circuit for a 10-bit look ahead carry adder is: 19 + 27 = 55

Conclusion

In conclusion, the number of AND gates required in the carry circuit for a 10-bit look ahead carry adder is 55. This includes the AND gates required for generating the carry and carry propagate signals, as well as the additional AND gates required for the carry lookahead logic.

Similar Computer Science Engineering (CSE) Doubts

A combinational digital circuit design is attempted using only NAND logic. The circuit has four inputs A,B,C,D, and one output Z. The output Z is required to be 1 (high) whenever either A = B = 1, or C = D = 1, or both.Which of the following conclusions is/are correct based on the given data?

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