A 4-bit parallel adder is a digital circuit that is used to perform arithmetic operations, specifically addition, on two 4-bit binary numbers. It is called a parallel adder because it performs the addition simultaneously on all the bits of the two input numbers.
The basic principle of a 4-bit parallel adder is the same as that of a 1-bit adder, which consists of two inputs (A and B) and a sum output (S). The input A and B can either be 0 or 1, and the sum output S is calculated based on the following truth table:
A | B | S |
---|---|---|
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
In a 1-bit adder, the sum output S is equal to the exclusive OR (XOR) of the two inputs A and B. The exclusive OR operation is a logical operation that returns a 1 if one of the inputs is 1 and the other is 0, and returns a 0 if both inputs are the same.
In a 4-bit parallel adder, the two input numbers are represented by four bits each, and the sum output is represented by a 5-bit number. The 4-bit parallel adder consists of four 1-bit adders, one for each bit of the input numbers. The sum output of each 1-bit adder is fed as an input to the next 1-bit adder, along with the carry-in bit (Cin) from the previous 1-bit adder. The carry-in bit represents the carry-over from the previous addition, which occurs when the sum output of a 1-bit adder is equal to 2 (i.e., 10 in binary).
The 4-bit parallel adder also includes a carry-out (Cout) bit, which is the carry-over from the addition of the most significant bit (MSB). The carry-out bit is important because it indicates when the sum of the two input numbers is greater than 15 (i.e., 1111 in binary), which is the maximum value that can be represented by a 4-bit number.
In summary, the 4-bit parallel adder is a digital circuit that is used to perform arithmetic operations, specifically addition, on two 4-bit binary numbers. It consists of four 1-bit adders, a carry-in bit, and a carry-out bit, and it performs the addition simultaneously on all the bits of the two input numbers. The 4-bit parallel adder is an important component in many digital systems and is widely used in computers and other electronic devices.