Final answer:
For the addition of two 17-bit numbers using minimum gates, we will need 17 half adders and 16 full adders.
Step-by-step explanation:
In order to add two 17-bit numbers using half adders and full adders, we need to break down both numbers into their individual bits and then add them bit by bit. Since each bit can be represented by a half adder, we will need 17 half adders for each 17-bit number. Additionally, since the carry out from each addition requires a full adder to propagate it to the next bit, we will need 16 full adders for the 17-bit numbers, resulting in a total of 17 half adders and 16 full adders.
When adding two 17-bit numbers, we use a combination of half adders and full adders to perform the binary addition. A half adder is used to add the least significant bits (LSBs) where there is no carry input, while full adders are used for all subsequent bits where the carry from the previous stage must be considered.
For the given problem, we require one half adder for the first bit (LSBs) since there is no carry from a previous addition at this stage. Every other bit will require a full adder since each will have to consider the carry bit from the bit before it. Therefore, for a 17-bit number, we will need 1 half adder and 16 full adders to handle the rest of the bits.
The correct answer is 16 half adders and 17 full adders, assuming that the 17th full adder is used to handle the final carry-out which may not be required in the addition, but typically included to support possible carry.