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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Figure 12 shows an 8-bit carry-skip adder consisting of four fixed-size blocks, each of size 2. 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. The adder structure is divided into blocks of consecutive stages with a simple ripple-carry scheme.

Figure 14 compares the delay information of true paths and that of false paths in the case of Hitachi 0. Figure 15 shows an array for operand, producing 2 outputs, where CSA indicates a carry-save adder having three multi-bit inputs and carlsoh multi-bit outputs.

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. 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.

Partial products are generated uan Radix-4 modified Booth recoding.

### Book Chapter – Han Carlson Adder – MSL

A multiply accumulator is generated by a combination of hardware algorithms for multipliers and constant-coefficient multipliers. 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. We employ Dadda’s strategy for constructing 7,3 counter trees. Figure 13 shows a bit carry-skip adder consisting of seven variable-size blocks.

If there are five or more blocks in a RCLA, 4 blocks afder grouped into a single superblock, with the second level of look-ahead applied to the superblocks.

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

A carry-skip adder reduces the carry-propagation time by skipping over groups of consecutive adder stages. The number of wiring tracks is a measure of wiring complexity. The above idea is applied to each of groups separately.

## Hybrid Han-Carlson adder

A block carry look-ahead adder BCLA is based on the above idea. 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 RB addition tree adde closely related to 4;2 compressor tree.

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.

### Hardware algorithms for arithmetic modules

The PPA stage then performs multi-operand addition for all the generated partial products and produces their sum in carry-save form. The hardware algorithms for constant-coefficient multiplication are based on multi-input 1-output addition algorithms i. Note here that the RB number should be encoded into a vector of binary digit in the standard binary-logic implementation.

There are many possible choices for the multiplier structure for a specific coefficient R. These expressions allow us to calculate all the carries in parallel from the operands.

## Hardware algorithms for arithmetic modules

The RCLA design is obtained by using multiple levels of carry look-ahead. The n-operand array consists of n-2 carry-save adder. Figure 5 is the parallel prefix graph of a Ladner-Fischer adder. On the other hand, the structure b shows a faster design, where two product terms are computed simultaneously in a single iteration. This reduces the ripple-carry delay through these blocks.

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 carslon partial product bits is reorganized to optimize the number of basic components.