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The number of full and half-adder required to add 16-bit numbers is
- a)8 half-adders, 8 full-adders
- b)1 half-adder, 15 full-adders
- c)16 half-adders, 0 full-adders
- d)4 half-adders, 12 full-adders
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The number of full and half-adder required to add 16-bit numbers isa)8...
To 16 bits number, 1 half and 15 full address or 16 full address are required.
Most Upvoted Answer
The number of full and half-adder required to add 16-bit numbers isa)8...
Explanation:
To add two 16-bit numbers, we need to perform addition of each corresponding bit, starting from the least significant bit (LSB) to the most significant bit (MSB).
Half-Adder:
A half-adder is a combinational circuit that adds two bits and produces a sum and carry. It has two inputs (A and B) and two outputs (Sum and Carry). The sum output is the XOR of the two inputs, and the carry output is the AND of the two inputs.
Full-Adder:
A full-adder is a combinational circuit that adds three bits (two inputs and a carry) and produces a sum and carry. It has three inputs (A, B, and Carry-in) and two outputs (Sum and Carry-out). The sum output is the XOR of the three inputs, and the carry-out is generated using a combination of AND, OR, and XOR gates.
Now, let's calculate the number of half-adders and full-adders required to add two 16-bit numbers.
Adding the LSB:
To add the LSB (bit 0), we only need a half-adder because there is no carry-in.
Adding the remaining bits:
For the remaining 15 bits (1 to 15), we need full-adders because there can be a carry-in from the previous bit addition.
So, the total number of half-adders required is 1 (for the LSB), and the total number of full-adders required is 15 (for the remaining bits).
Hence, the correct answer is option 'B' - 1 half-adder and 15 full-adders.
To add two 16-bit numbers, we need to perform addition of each corresponding bit, starting from the least significant bit (LSB) to the most significant bit (MSB).
Half-Adder:
A half-adder is a combinational circuit that adds two bits and produces a sum and carry. It has two inputs (A and B) and two outputs (Sum and Carry). The sum output is the XOR of the two inputs, and the carry output is the AND of the two inputs.
Full-Adder:
A full-adder is a combinational circuit that adds three bits (two inputs and a carry) and produces a sum and carry. It has three inputs (A, B, and Carry-in) and two outputs (Sum and Carry-out). The sum output is the XOR of the three inputs, and the carry-out is generated using a combination of AND, OR, and XOR gates.
Now, let's calculate the number of half-adders and full-adders required to add two 16-bit numbers.
Adding the LSB:
To add the LSB (bit 0), we only need a half-adder because there is no carry-in.
Adding the remaining bits:
For the remaining 15 bits (1 to 15), we need full-adders because there can be a carry-in from the previous bit addition.
So, the total number of half-adders required is 1 (for the LSB), and the total number of full-adders required is 15 (for the remaining bits).
Hence, the correct answer is option 'B' - 1 half-adder and 15 full-adders.
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The number of full and half-adder required to add 16-bit numbers isa)8 half-adders, 8 full-addersb)1 half-adder, 15 full-addersc)16 half-adders, 0 full-addersd)4 half-adders, 12 full-addersCorrect answer is option 'B'. Can you explain this answer?
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