A half adder is a basic digital circuit used in binary addition. It takes in two binary inputs (typically represented by 'A' and 'B') and produces two outputs: the sum ('S') and the carry ('C'). The half adder can only add two binary digits and does not consider any carry-in from previous additions.
The truth table for a half adder is as follows:
A B Sum (S) Carry (C)
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
As you can see, the sum (S) is the XOR of the two input bits (A and B), and the carry (C) is the AND of the same input bits. The XOR operation (exclusive OR) outputs a 1 if the two inputs are different and 0 if they are the same. The AND operation outputs a 1 only when both inputs are 1.
To perform binary addition using a half adder, you would connect multiple half adders together to handle multi-bit binary numbers. The carry output of each half adder becomes the carry-in for the next adder. This way, you can add binary numbers of any length.
Here's an example of a 2-bit binary addition using two half adders:
sql
Copy code
A1 B1
\ /
\/ (carry-in to the first half adder is 0)
+ A0 B0
\ /
\/ (carry-out from the first half adder becomes carry-in to the second half adder)
_______________
Sum1 Sum0 Carry
For instance, if A1 = 1, B1 = 1, A0 = 0, and B0 = 1, the result would be Sum1 = 1, Sum0 = 0, and Carry = 1, indicating the final sum is 110 binary, which is equivalent to 6 in decimal.
It's important to note that the half adder can handle the addition of two bits but does not consider any carry from previous additions. To perform addition of multi-bit binary numbers, you would need to use full adders, which take into account both the current bit and the carry from the previous bit.