Guy Even †. February 1, Abstract. We present a self-contained and detailed description of the parallel-prefix adder of Ladner and Fischer. Very little. Abstract. Ladner –Fischer adder is one of the parallel prefix adders. Parallel prefix adders are used to speed up the process of arithmetic operation. Download scientific diagram | Modified Ladner Fischer Adder from publication: Implementation of Efficient Parallel Prefix Adders for Residue Number System | In .

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Hardware algorithms for arithmetic modules

The RB addition tree is closely related to 4;2 compressor tree. Please note that the delay information of carry-skip adders in Reference data page is simply estimated by using false paths instead of true paths.

Once the incoming carry is known, we need only to select the correct set of outputs out fiwcher the two sets without waiting for the carry to further propagate through the k positions. These hardware algorithms are also used to generate multipliers, constant-coefficient multipliers and multiply accumulators.

Table 1 shows hardware algorithms that can be selected for multi-operand adders in AMG, where the bit-level optimized design indicates that the matrix of partial product bits is reorganized to optimize the number of basic components. Figure 17 shows an operand balanced delay tree, where CSA indicates a carry-save adder having three multi-bit inputs and two multi-bit outputs. The Wallace tree guarantees the lowest overall delay but requires the largest number of wiring tracks vertical feedthroughs between adjacent bit-slices.

Figure 2 shows the parallel prefix graph of a bit RCLA, where the symbol solid circle indicates an extension of the fundamental carry operator described at Parallel prefix adders. Note here that the RB number should be ladnwr into a vector of binary digit in the standard binary-logic implementation.

Redundant binary RB addition tree has a more regular structure than an ordinary CSA tree made of 3,2 counters because the RB partial products are added up in the binary tree form by RB adders. To reduce the hardware complexity, we allow the use of 6,35,34,33,2and 2,2 counters in addition to 7,3 counters.


Array is a straightforward way to accumulate partial products using a number of adders. This adder is the extreme case of maximum logic depth and minimum area. To reduce the hardware complexity, we allow the use of 2,2 counters in addition to 3,2 counters.

Hardware algorithms for arithmetic modules

Figure 15 shows an array for operand, producing 2 outputs, where CSA indicates a carry-save adder having three multi-bit inputs and two multi-bit outputs. Another way to design a practical carry look-ahead adder is to reverse the basic design principle of the RCLA, that is, to ripple carries within blocks but to generate carries between blocks by look-ahead.

Therefore, let Gi and Pi denote the generation and propagation at the ith stage, we have: Generalized MAC Figure Ficher fixed block ladned should be selected so that the time for the longest carry-propagation chain can be minimized. A multiply accumulator is generated by a combination of hardware algorithms for multipliers and constant-coefficient multipliers. Arithmetic Module Generator AMG supports various hardware algorithms for two-operand adders and multi-operand adders.

As a result, AMG supports such hardware algorithms for constant-coefficient multiplication, where the range of R is from -2 31 to 2 31 The structure a illustrates a typical situation, where the MAC is used to perform a multiply-add operation in an iterative fashion.

The idea of the ripple-block carry look-ahead addition is to lessen the fan-in and fan-out difficulties inherent in carry look-ahead adders. The fundamental carry operator is addder as Figure 4.

This optimal organization of block size includes L blocks with sizes k1, k2, Balanced delay tree requires the smallest number of wiring tracks but has the highest overall delay compared with the Wallace tree and the overturned-stairs tree. On the other hand, the structure b shows a fiscuer design, where fischdr product terms are computed simultaneously in a single iteration.

One set assumes that the eventual incoming carry will be zero, while the other assumes that it will be one. Figure 12 shows an 8-bit carry-skip adder consisting of four fixed-size blocks, each of size 2. There xdder many possible choices for the multiplier structure for adddr specific coefficient R. The adder structure is divided into blocks of consecutive stages with a simple ripple-carry scheme. We employ Dadda’s strategy for constructing 7,3 counter trees. Figure 14 compares the delay information of true paths and that of false paths in the case of Hitachi 0.


A constant-coefficient multiplier is given as a part of MACs as follow. You can further increase the number of product terms computed in a single cycle depending on your target applications.

Figure 1 shows a ripple carry adder for n-bit operands, producing n-bit sum outputs and a carry out. Figure 13 shows a bit carry-skip adder consisting of seven variable-size blocks.

Figure 18 shows an operand overturned-stairs tree, where CSA indicates a carry-save adder having three multi-bit inputs and two multi-bit outputs.

Figure 19 shows an operand 4;2 compressor tree, where 4;2 indicates a carry-save adder having four multi-bit inputs and two multi-bit outputs. The basic idea in the conditional sum adder is to generate two sets of outputs for a given group of operand bits, say, k bits. The number of wiring tracks is a measure of wiring complexity.

Figure 22 shows a n-term fisched accumulator. The carry-save form is converted to the fuscher binary output by an FSA. This signal can be used to allow an incoming carry to skip all the stages within the block and generate a block-carry-out.

Parallel Prefix Adders A Case Study – ppt video online download

Figure 7 is the parallel prefix graph of a Brent-Kung adder. Wallace tree is known for their optimal computation time, when adding multiple operands to two outputs using carry-save adders. Dadda tree is based on 3,2 counters. In this generator, the group lzdner follow the simple arithmetic progression 1, 1, 2, 3,