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The hardware unit that performs the operation is known as a multiplier–accumulator (MAC unit); the operation itself is also often called a MAC or a MAD operation. The MAC operation modifies an accumulator a : a ← a + ( b × c ) {\displaystyle a\gets a+(b\times c)}
This can be used at multiple levels to make even larger adders. For example, the following adder is a 64-bit adder that uses four 16-bit CLAs with two levels of lookahead carry units. Other adder designs include the carry-select adder, conditional sum adder, carry-skip adder, and carry-complete adder.
In a computer's central processing unit (CPU), the accumulator is a register in which intermediate arithmetic logic unit results are stored.. Without a register like an accumulator, it would be necessary to write the result of each calculation (addition, multiplication, shift, etc.) to cache or main memory, perhaps only to be read right back again for use in the next operation.
The Brent–Kung adder is a parallel prefix adder (PPA) form of carry-lookahead adder (CLA). Proposed by Richard Peirce Brent and Hsiang Te Kung in 1982 it introduced higher regularity to the adder structure and has less wiring congestion leading to better performance and less necessary chip area to implement compared to the Kogge–Stone adder (KSA).
The method is slow, however, as it involves many intermediate additions. These additions are time-consuming. Faster multipliers may be engineered in order to do fewer additions; a modern processor can multiply two 64-bit numbers with 6 additions (rather than 64), and can do several steps in parallel. [citation needed]
4-bit parallel binary accumulator three-state 20 SN74LS681: 74x682 1 ... 8-bit serial/parallel multiplier with adder/subtractor 20 74F784: 74x785 1
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.
By calculating a small block of entries simultaneously, the following loop reuses each loaded value twice, so that the inner loop has four loads and four multiply–adds, thus solving problem #2. By carrying four accumulators simultaneously, this code can keep a single floating point adder with a latency of 4 busy nearly all the time (problem #1).