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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.
4-bit adder with logical block diagram shown Decimal 4-digit ripple carry adder. FA = full adder, HA = half adder. It is possible to create a logical circuit using multiple full adders to add N-bit numbers. Each full adder inputs a , which is the of the previous adder.
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
"Feedback Integrating System" by Charles B Brahm: The entire top half of its Fig 1 is a delta-sigma modulator. Box #10 is a two-input integrator. The 4-bit analog-to-digital quantizer uses designations "S" (sign), "1", "2", and "4" for each bit. Each "F" stands for flip-flop and each "G" is a gate, controlled by the 110 kHz oscillator.
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 few systems that calculate the majority function on an even number of inputs are often biased towards "0" – they produce "0" when exactly half the inputs are 0 – for example, a 4-input majority gate has a 0 output only when two or more 0's appear at its inputs. [1]
In some configurations, the phase output is taken from the output of the register which introduces a one clock cycle latency but allows the adder to operate at a higher clock rate. [2] Figure 2: Normalized phase accumulator output. The adder is designed to overflow when the sum of the absolute value of its operands exceeds its capacity (2 N − ...
Three-bit full adder (add with carry) using five Fredkin gates. Three-bit full adder (add with carry) using five Fredkin gates. The "garbage" output bit g is (p NOR q) if r = 0, and (p NAND q) if r = 1. Inputs on the left, including two constants, go through three gates to quickly determine the parity.