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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### Book Chapter – Han Carlson Adder – MSL

In this generator, we employ a minimum length encoding based on positive-negative representation. Figure 14 compares the delay information of true cralson and that of false paths in the case of Hitachi 0. A 7,3 counter tree is based on 7,3 counters.

We consider here the use of special number representation called Signed-Weight SW number system, which is useful for constructing compact PPAs. The above idea is applied carpson each of groups separately. 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.

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 PPA stage then performs multi-operand addition for all the generated partial products and produces their sum in carry-save form.

## Hardware algorithms for arithmetic modules

This adder structure has minimum logic depth, and full binary tree with minimum fun-out, resulting in a fast adder but with a addre area. Figure 5 is the parallel prefix graph of a Ladner-Fischer adder.

Note here that the RB number should be encoded into a vector of binary digit in the standard binary-logic implementation. Addee main idea behind carry look-ahead addition is an attempt to generate all incoming carries in parallel and avoid waiting until the correct carry propagates from the stage FA of the adder where it has been generated. Dadda tree is based on 3,2 counters. A multiply accumulator is generated by a combination of hardware algorithms for multipliers and constant-coefficient multipliers.

Wallace tree is known for their optimal computation time, when adding multiple operands to two outputs using carry-save 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 most straightforward implementation of a final stage adder for two n-bit operands is a ripple carry adder, which requires n full adders FAs.

The hardware algorithms for constant-coefficient multiplication are based on multi-input 1-output addition algorithms i. 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.

There are many possible choices for the multiplier structure for a specific addr R. Each group generates two sets of sum bits and an outgoing carry. The Wallace tree guarantees the lowest overall delay but requires addfr largest number of wiring tracks vertical feedthroughs between adjacent bit-slices. Each set includes k sum bits and an outgoing carry. This process can, in principle, be continued until a group of size 1 is reached.

Partial products are generated with Radix-4 modified Booth recoding. When the incoming carry into the group is assigned, its final value is selected out of the two sets.

The carry-skip adder is usually comparable in speed to the carry look-ahead technique, but it requires less chip area and consumes less power. Figure 13 shows a bit carry-skip adder consisting of seven variable-size blocks. Figure 7 is the parallel prefix graph of a Brent-Kung adder. A carry-skip adder reduces adcer carry-propagation time by skipping over groups of consecutive adder stages.

## Hybrid Han-Carlson adder

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

Once the incoming carry is known, we need only to select the correct set of outputs out of the two sets without waiting for the carry to further propagate through the k positions.

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. The adder structure is divided into blocks of consecutive stages with a simple ripple-carry scheme.

A constant-coefficient multiplier is given as a part of MACs as follow. 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.

The RCLA design is obtained by using multiple levels of carry look-ahead. Figure 22 shows a n-term multiply accumulator. The complexity of multiplier structures significantly caroson with the coefficient value R.

If there are five or more blocks in a RCLA, 4 blocks are grouped into a single superblock, with the second level of look-ahead applied to the superblocks. A block carry look-ahead adder Hsn is based on the above idea.

The structure a illustrates a typical situation, where the MAC is used to perform a multiply-add operation in an iterative fashion.

One set assumes that the eventual incoming carry will be zero, while the other assumes dader it will be one. Figure 8 is the parallel prefix graph of a Han-Carlson adder. 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. To reduce the hardware complexity, we allow the use of 2,2 counters in addition to 3,2 counters.

AMG provides constant-coefficient multipliers in the form: Figure 17 shows an operand balanced darlson tree, where CSA indicates a carry-save adder having three multi-bit inputs and two multi-bit outputs. Arithmetic Module Generator AMG supports various hardware algorithms for two-operand adders and multi-operand adders.

Finally, the carry-save form is converted to the corresponding binary output at FSA. In the following, we briefly describe the hardware algorithms that can be handled by AMG.

Array is a straightforward way to accumulate partial products using a number of adders. The Booth recoding of the addfr reduces the number of partial products and hence has a possibility of reducing the amount of hardware involved and the execution time. Figure 6 is the parallel nan graph of a Kogge-Stone adder.