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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Partial products are generated with Radix-4 modified Booth recoding. This reduces the ripple-carry delay through these blocks. Figure 1 shows a ripple carry adder for n-bit operands, producing n-bit sum outputs and a carry out. You can further increase the number of product terms computed in a single cycle carlaon on your target applications.

On the other hand, the structure b shows a faster design, where two product terms are computed simultaneously in a single iteration. The Wallace tree guarantees the lowest overall delay but requires the largest number of wiring tracks vertical feedthroughs between adjacent bit-slices. Given the matrix of partial product bits, the number of bits in each column is reduced to minimize the number of cwrlson and 2,2 counters.

Hardware algorithms for arithmetic modules

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. This process can, in principle, be continued until a group of size 1 is reached.

The n-operand array consists of n-2 carry-save adder. The structure a illustrates a typical situation, where the MAC is used to perform a multiply-add operation in an iterative fashion. We consider here the use of special number representation called Signed-Weight SW number system, which is useful for constructing compact PPAs. Arithmetic Module Generator AMG supports various hardware algorithms for two-operand adders and multi-operand adders.

Figure 12 shows an 8-bit carry-skip adder consisting of four fixed-size blocks, each of size 2. In other words, a carry is generated if both operand bits are 1, and an incoming carry is propagated if one of the operand bits is 1 and the other is 0.

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Book Chapter – Han Carlson Adder – MSL

AMG provides multiply accumulators in the form: Array is a straightforward way to accumulate partial products using a number of adders. A carry-skip adder reduces the carry-propagation time by skipping over groups of consecutive adder stages. The complexity of multiplier calson significantly varies with the coefficient value R. When the incoming carry into the group is assigned, its final value is selected out of the two sets.

The PPG stage first generates partial yan from the multiplicand and multiplier in parallel. At present, the combination of CSD Canonic Signed-Digit coefficient encoding technique with the SW-based PPAs seems to provide the practical hardware implementation of fast constant-coefficient multipliers.

This adder structure has minimum logic depth, and full binary tree with minimum fun-out, resulting in a fast adder but with a large area. Adser 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.

The block size m is fixed to 4 in the generator. To reduce the hardware complexity, we allow the use of 6,35,34,33,2and 2,2 counters in addition to 7,3 counters. The underlying strategy of the carry-select adder is similar to that of the conditional-sum adder.

Dadda tree is based on 3,2 counters. This adder has a hybrid design combining stages from the Brent-Kung and Kogge-Stone adder.

This signal can be used to allow an incoming carry to skip all the stages within the block and generate a block-carry-out.

The Booth recoding of the multiplier reduces the number of partial products and hence has a possibility of reducing the amount of hardware involved and the execution time.

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. 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.

As a result, AMG supports such hardware algorithms for constant-coefficient multiplication, where the range of R is from -2 31 to 2 31 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.


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. 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.

Each set includes k sum bits and an outgoing carry. The fixed block size should be selected so that the time for the longest carry-propagation chain can be minimized.

The fundamental carry operator is represented as Figure 4. The hardware algorithms for constant-coefficient multiplication are based on multi-input 1-output addition algorithms i.

In this generator, we employ a minimum length encoding based on positive-negative representation. Unlike csrlson 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. Figure 8 is the parallel prefix graph of a Han-Carlson adder. One set assumes that the incoming carry into the group is 0, the other assumes that it is 1. A adderr carry look-ahead adder RCLA consists of N m-bit blocks arranged in such a way that carries within blocks are generated by carry look-ahead but carries between blocks are rippled.

Note here that the RB number should be encoded into a vector of binary digit in the standard binary-logic implementation.

Hybrid Han-Carlson adder

Each group generates two sets of sum bits and an outgoing carry. Figure 14 compares the delay information of true paths and that of false paths in the case of Hitachi 0. The adder structure is divided carlspn blocks of consecutive stages with a simple ripple-carry scheme.

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.