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The sum-output from the second half adder is the final sum output of the full adder and the output from the OR gate is the final carry output (). The critical path of a full adder runs through both XOR gates and ends at the sum bit . Assumed that an XOR gate takes 1 delays to complete, the delay imposed by the critical path of a full adder is ...
The number of inputs of the AND-gate is equal to the width of the adder. For a large width, this becomes impractical and leads to additional delays, because the AND-gate has to be built as a tree. A good width is achieved, when the sum-logic has the same depth like the n-input AND-gate and the multiplexer. 4 bit carry-skip adder.
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.
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 ...
Wallace multipliers reduce as much as possible on each layer, whereas Dadda multipliers try to minimize the required number of gates by postponing the reduction to the upper layers. [ 1 ] Wallace multipliers were devised by the Australian computer scientist Chris Wallace in 1964.
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.
A majority gate returns true if and only if more than 50% of its inputs are true. For instance, in a full adder, the carry output is found by applying a majority function to the three inputs, although frequently this part of the adder is broken down into several simpler logical gates.
The 3-input Fredkin gate is functionally complete reversible gate by itself – a sole sufficient operator. There are many other three-input universal logic gates, such as the Toffoli gate. In quantum computing, the Hadamard gate and the T gate are universal, albeit with a slightly more restrictive definition than that of functional completeness.