what is the difference between the following:
1- Half adder and full adder
2- Half Subtractor and Full Subtractor
The correct answer and explanation is :
1. Half Adder vs Full Adder
A half adder and a full adder are both combinational circuits used for binary addition. The key difference between them lies in the number of inputs and the ability to handle carry from previous calculations.
- Half Adder: A half adder adds two single binary digits (bits) and produces a sum and a carry. It has two inputs (A and B), and two outputs: the sum (S) and the carry (C). The carry is generated when both bits are 1 (i.e., 1+1 = 10 in binary). The sum is the XOR of the two bits, and the carry is the AND of the two bits.
- Truth Table:
- A = 0, B = 0 → Sum = 0, Carry = 0
- A = 0, B = 1 → Sum = 1, Carry = 0
- A = 1, B = 0 → Sum = 1, Carry = 0
- A = 1, B = 1 → Sum = 0, Carry = 1
- Full Adder: A full adder is an extension of the half adder. It adds three inputs: two binary digits (A and B) and an additional carry input (Cin). It produces two outputs: the sum (S) and the carry (Cout). The full adder takes into account the carry from the previous stage and adds it to the sum.
- Truth Table:
- A = 0, B = 0, Cin = 0 → Sum = 0, Cout = 0
- A = 0, B = 1, Cin = 0 → Sum = 1, Cout = 0
- A = 1, B = 0, Cin = 0 → Sum = 1, Cout = 0
- A = 1, B = 1, Cin = 0 → Sum = 0, Cout = 1
- (And similarly for other combinations including Cin)
2. Half Subtractor vs Full Subtractor
A half subtractor and a full subtractor are used for binary subtraction. The primary difference lies in their ability to handle borrow and the number of inputs.
- Half Subtractor: A half subtractor is used to subtract two binary digits (bits). It has two inputs: A (minuend) and B (subtrahend). It produces two outputs: the difference (D) and the borrow (B). The borrow occurs when the subtrahend (B) is greater than the minuend (A).
- Truth Table:
- A = 0, B = 0 → Difference = 0, Borrow = 0
- A = 0, B = 1 → Difference = 1, Borrow = 1
- A = 1, B = 0 → Difference = 1, Borrow = 0
- A = 1, B = 1 → Difference = 0, Borrow = 0
- Full Subtractor: A full subtractor works similarly to a half subtractor but can also handle an additional borrow input (Bin). This allows it to subtract not only two binary digits but also the borrow from a previous stage.
- Truth Table:
- A = 0, B = 0, Bin = 0 → Difference = 0, Borrow = 0
- A = 0, B = 1, Bin = 0 → Difference = 1, Borrow = 1
- A = 1, B = 0, Bin = 0 → Difference = 1, Borrow = 0
- A = 1, B = 1, Bin = 0 → Difference = 0, Borrow = 0
- (And similarly for other combinations including Bin)
Conclusion:
- Half Adder: Adds two bits, does not handle carry-in.
- Full Adder: Adds two bits and carry-in, generates carry-out.
- Half Subtractor: Subtracts two bits, does not handle borrow-in.
- Full Subtractor: Subtracts two bits and borrow-in, generates borrow-out.
The full versions are more flexible because they can process carry/borrow from previous stages.