Full Adder
Full adder[edit source | editbeta]
Schematic symbol for a 1-bit full adder with Cin and Cout drawn on sides of block to emphasize their use in a multi-bit adder
A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers, often written as A,B, and Cin; A and B are the operands, and Cin is a bit carried in from the next less significant stage.[2] The full-adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. bit wide binary numbers. The circuit produces a two-bit output, output carry and sum typically represented by the signals Cout and S, where . The one-bit full adder's truth table is:
Full-adder logic diagram
Inputs
Outputs
A
B
Cin
Cout
S
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
A full adder can be implemented in many different ways such as with a custom transistor-level circuit or composed of other gates. One example implementation is with and .
In this implementation, the final OR gate before the carry-out output may be replaced by an XOR gate without altering the resulting logic. Using only two types of gates is convenient if the circuit is being implemented using simple IC chips which contain only one gate type per chip. In this light, Cout can be implemented as .
A full adder can be constructed from two half adders by connecting A and B to the input of one half adder, connecting the sum from that to an input to the second adder, connecting Ci to the other input and OR the two carry outputs. Equivalently, S could be made the three-bit XOR of A, B, and Ci, and Cout could be made the three-bit majority function of A, B, and Cin.
BCD (Binary Coded Decimal) Adder is a digital combinational circuit that is used for the addition of two numbers in binary coded decimal arithmetic's. BCD is a class of binary encodings of decimal numbers where each decimal digit is shown
Schematic symbol for a 1-bit full adder with Cin and Cout drawn on sides of block to emphasize their use in a multi-bit adder
A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers, often written as A,B, and Cin; A and B are the operands, and Cin is a bit carried in from the next less significant stage.[2] The full-adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. bit wide binary numbers. The circuit produces a two-bit output, output carry and sum typically represented by the signals Cout and S, where . The one-bit full adder's truth table is:
Full-adder logic diagram
Inputs
Outputs
A
B
Cin
Cout
S
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
A full adder can be implemented in many different ways such as with a custom transistor-level circuit or composed of other gates. One example implementation is with and .
In this implementation, the final OR gate before the carry-out output may be replaced by an XOR gate without altering the resulting logic. Using only two types of gates is convenient if the circuit is being implemented using simple IC chips which contain only one gate type per chip. In this light, Cout can be implemented as .
A full adder can be constructed from two half adders by connecting A and B to the input of one half adder, connecting the sum from that to an input to the second adder, connecting Ci to the other input and OR the two carry outputs. Equivalently, S could be made the three-bit XOR of A, B, and Ci, and Cout could be made the three-bit majority function of A, B, and Cin.
BCD (Binary Coded Decimal) Adder is a digital combinational circuit that is used for the addition of two numbers in binary coded decimal arithmetic's. BCD is a class of binary encodings of decimal numbers where each decimal digit is shown