An XOR gate, short for Exclusive OR gate, is a digital logic gate that takes two binary inputs (0 or 1) and produces a single binary output based on the following logic:
If the number of input values that are 1 is odd, the output is 1.
If the number of input values that are 1 is even, the output is 0.
Symbolically, an XOR gate is represented as ⊕ or sometimes as ⊻.
Here's the truth table for an XOR gate:
Input A Input B Output
0 0 0
0 1 1
1 0 1
1 1 0
The significance of XOR gates in binary addition lies in their ability to determine whether two bits being added are the same or different. When performing binary addition, each bit of the sum is calculated using an XOR gate, and the carry from the previous addition step is computed using an AND gate. The XOR gate helps in deciding whether a carry should be generated or not based on the individual bits being added.
For example, let's consider the binary addition of two numbers: 1011 and 1101.
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Copy code
1 0 1 1 (1011)
+ 1 1 0 1 (1101)
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1 0 0 0 0 (10000)
In this addition, each bit position is calculated using an XOR gate, and the carry is calculated using an AND gate. The XOR gate determines whether a bit position contributes to the sum or not, and the carry determines whether a carry should be propagated to the next bit position.
In summary, XOR gates are essential components in binary addition because they enable us to combine individual bits while considering their differences, and they play a crucial role in determining both the sum and the carry during the addition process.