Han Carlson Adder(Professor Han invented Han Carlson adder in part of his Ph. D. dissertation). currently widely used in Intel Pentium Micro. Download scientific diagram | (a) Han-Carlson (HC) adder; from publication: Power-aware Design of Logarithmic Prefix Adders in Sub-threshold Regime: A. Key Words – Parallel Prefix Adders, Han-Carlson Adder, area, prefix computation, Power Consumption, delay. 1. Introduction. VLSI binary adders are critically.

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Wallace tree is known for their optimal computation time, when adding multiple operands to two outputs using carry-save adders. The fundamental carry operator is represented as Figure 4. 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. Generalized MAC Figure The block size m is fixed to 4 in the generator.

Given the matrix of partial product bits, the number of bits in each column is reduced to minimize the number of 3,2 and 2,2 counters. This signal can be used to allow an incoming carry to skip all the stages within the block and generate a block-carry-out. Unlike the conditional-sum adder, the sizes of the kth group is chosen so as to equalize the delay of the ripple-carry within the group and the delay of the carry-select chain from group 1 to group k.

The n-operand array consists of n-2 carry-save adder.

## Hybrid Han-Carlson adder

Figure 2 shows the parallel prefix graph of a bit RCLA, where the symbol solid circle indicates an extension of the fundamental carry operator adeer at Parallel prefix adders. This optimal organization of block size includes L blocks with sizes k1, k2, Figure 5 is the parallel prefix graph of a Ladner-Fischer adder.

One set assumes that the eventual incoming carry will be zero, while the other assumes that it will be one. Figure 16 shows an operand Wallace tree, where CSA hna a carry-save adder having three multi-bit inputs and two multi-bit outputs.

Figure 8 is the parallel prefix graph of a Han-Carlson adder. Each set includes k sum bits and an outgoing carry. A multiply accumulator is generated by a combination of hardware algorithms for multipliers and constant-coefficient multipliers.

## Hardware algorithms for arithmetic modules

To reduce the hardware complexity, we allow the use of 6,35,34,33,2and 2,2 counters in addition to 7,3 counters.

In other words, a carry is generated if both dader bits are 1, and an incoming carry is propagated if one of the operand bits is 1 and the other is 0. The PPA stage then performs multi-operand addition for all the generated partial products and produces their sum hann carry-save form. 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.

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. A carry-skip adder reduces the carry-propagation time by skipping over groups of consecutive adder stages.

Figure 22 shows a n-term multiply accumulator. At present, the combination of CSD Canonic Signed-Digit coefficient encoding technique with the SW-based PPAs seems to provide carlsoj practical hardware implementation of fast constant-coefficient multipliers. Arithmetic Module Generator AMG supports various hardware algorithms for two-operand adders and multi-operand adders. Afder are many possible choices for the multiplier structure for a specific coefficient R.

The adder structure is divided into blocks of consecutive stages with a simple ripple-carry scheme. Note here that the RB number should be encoded into a vector of binary digit in the standard binary-logic implementation.

The equation can be interpreted as stating that there is a carry either if one is generated at that stage or if one is propagated from the preceding stage. This process can, in principle, be continued until a group of size 1 is reached.

This adder is the extreme case of maximum logic depth and minimum area. 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.

### Book Chapter – Han Carlson Adder – MSL

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. The fixed block size should be selected so that the adderr for the longest carry-propagation chain can be minimized. AMG provides constant-coefficient multipliers in the form: The above idea is applied to each of groups separately.

The PPG stage first generates partial products from the multiplicand and multiplier in xdder. In this generator, we employ a minimum length encoding based on positive-negative representation. The structure a illustrates a typical situation, where the MAC is used to perform a multiply-add operation in an iterative fashion.

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. 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.

The carry-save form is converted to the corresponding binary output by an FSA.

You can further increase the number of product terms computed in a single cycle depending on your target applications. The underlying strategy of the carry-select adder is similar to that of the conditional-sum adder. The hardware algorithms for constant-coefficient multiplication carlsin based on multi-input 1-output addition algorithms i. Figure 12 shows an 8-bit carry-skip adder consisting of four fixed-size blocks, each of size 2.

A parallel prefix adder can be represented as a parallel prefix graph consisting of carry operator nodes. Redundant binary RB farlson 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.

The Wallace tree guarantees the lowest overall delay but requires the largest number of wiring csrlson vertical feedthroughs between adjacent bit-slices. The main idea behind carry look-ahead addition is an attempt to generate all incoming carries in parallel and avoid waiting until the correct carry addeer from the stage FA of the adder where it has been generated.

One set assumes that the incoming carry into the group is 0, the other assumes that it is 1.