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With the addition of an OR gate to combine their carry outputs, two half adders can be combined to make a full adder. [2] The half adder adds two input bits and generates a carry and sum, which are the two outputs of a half adder. The input variables of a half adder are called the augend and addend bits. The output variables are the sum and carry.
A (with A i set to invert; B i set to zero; and D = 0) −A (with A i set to invert; B i set to zero; and D = 1) B (with B i set to invert; A i set to zero; and D = 0) −B (with B i set to invert; A i set to zero; and D = 1) By adding more logic in front of the adder, a single adder can be converted into much more than just an adder—an ALU.
The basic Fredkin gate [3] is a controlled swap gate (CSWAP gate) that maps three inputs (C, I 1, I 2) onto three outputs (C, O 1, O 2). The C input is mapped directly to the C output. If C = 0, no swap is performed; I 1 maps to O 1, and I 2 maps to O 2. Otherwise, the two outputs are swapped so that I 1 maps to O 2, and I 2 maps to O 1. It is ...
So the result is four possible outputs of C and R. If one were to use base 3, the size would increase to 3×3, or nine possible outputs. The first "addition" example above is called a half-adder. A full-adder is when the carry from the previous operation is provided as input to the next adder.
The Dadda multiplier is a hardware binary multiplier design invented by computer scientist Luigi Dadda in 1965. [1] It uses a selection of full and half adders to sum the partial products in stages (the Dadda tree or Dadda reduction) until two numbers are left.
Add a half adder for weight 2, outputs: 1 weight-2 wire, 1 weight-4 wire; Add a full adder for weight 4, outputs: 1 weight-4 wire, 1 weight-8 wire; Add a full adder for weight 8, and pass the remaining wire through, outputs: 2 weight-8 wires, 1 weight-16 wire; Add a full adder for weight 16, outputs: 1 weight-16 wire, 1 weight-32 wire
For example, if we add 1 plus 1 in binary, we expect a two-bit answer, 10 (i.e. 2 in decimal). Since the trailing sum bit in this output is achieved with XOR, the preceding carry bit is calculated with an AND gate. This is the main principle in Half Adders. A slightly larger Full Adder circuit may be chained together in order to add longer ...
A conditional sum adder [3] is a recursive structure based on the carry-select adder. In the conditional sum adder, the MUX level chooses between two n/2-bit inputs that are themselves built as conditional-sum adder. The bottom level of the tree consists of pairs of 2-bit adders (1 half adder and 3 full adders) plus 2 single-bit multiplexers.