The number of full and half-adders required to add 16-bit numbers is :

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NIELIT Scientific Assistant CS 5 Dec 2021 Official Paper
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  1. 8 half-adders, 8 full-adders
  2. 1 half-adder, 15 full-adders
  3. 16 half-adders, 0 full-adders
  4. 4 half-adders, 12 full-adders

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Option 2 : 1 half-adder, 15 full-adders
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The correct answer is 1 half-adder, 15 full-adders.

Key Points

  • A 16-bit binary adder requires 1 half-adder and 15 full-adders.
  • A half-adder is used to add the least significant bit (LSB), which does not require a carry-in bit.
  • Full-adders are used for the remaining bits, which must account for both the carry-in and carry-out bits.
  • The structure ensures efficient addition of binary numbers with proper handling of carry bits.

additional-information-image Additional Information

  • Full-adders can add three bits together: two significant bits and one carry bit from the previous stage.
  • Half-adders can add two bits together but cannot handle carry-in bits.
  • In a 16-bit addition, the first stage uses a half-adder, and the subsequent 15 stages use full-adders.
  • This configuration minimizes the number of adders required while ensuring correct binary addition.
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