If half adders and full adders are implemented using gates, then for the…
2015
If half adders and full adders are implemented using gates, then for the addition of two 17 bit numbers (using minimum gates) the number of half adders and full adders required will be, ISRO 2015
- A.
0, 17
- B.
16, 1
- C.
1, 16
- D.
8, 8
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Correct answer: C
To add two n-bit numbers using ripple carry adders, we need one Half Adder (HA) for the least significant bit (LSB) and n-1 Full Adders (FA) for the remaining bits. This is because the LSB addition does not require a carry-in, while all subsequent bit positions do.\nFor 17-bit numbers:\n- The LSB (bit 0) uses 1 Half Adder.\n- The remaining 16 bits (bits 1 to 16) each require a Full Adder to handle the carry-in from the previous position.\nThus, we need 1 Half Adder and 16 Full Adders. Option A is incorrect because it suggests no HAs, which would require a carry-in for the first bit. Option B reverses the count. Option D incorrectly splits the adders equally.
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