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seminar surveyer
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19-01-2011, 03:43 PM

.doc   DESIGN OF EFFICIENT MULTIPLIER USING VHDL.doc (Size: 1.57 MB / Downloads: 232)

MR. Arun Sharma

There are different entities that one would like to optimize when designing a VLSI circuit. These entities can often not be optimized simultaneously, only improve one entity at the expense of one or more others.The design of an efficient multiplier circuit in terms of power, area, and speed simultaneously, has become a very challenging problem. Power dissipation is recognized as a critical parameter in modern VLSI design field. In Very Large Scale Integration, low power VLSI design is necessary. Multiplication occurs frequently in finite impulse response filters, fast Fourier transforms, convolution, and other important DSP and multimedia kernels. The objective of a good multiplier is to provide a physically compact, good speed and low power consuming chip. To save significant power consumption of a VLSI design, it is a good direction to reduce its dynamic power that is the major part of total power dissipation. In this thesis, we propose high speed low-power multiplier algorithms. The booth multiplier will reduce the number of partial products generated by a factor of 2. The adder will avoid the unwanted addition and thus minimize the switching power dissipation. The proposed high speed low power multiplier can attain speed improvement and power reduction in the Booth encoder when compared with the conventional array multipliers.

This thesis presents an efficient implementation of high speed multiplier using the array multiplier,shift & add algorithm,Booth multipliet,pyramid algorithm & modify pyramid algorithm. In this thesis we compare the working of the these multipliers by implementing each of them separately.



Multipliers are key components of many high performance systems such as FIR filters, microprocessors, digital signal processors, etc. A system’s performance is generally determined by the performance of the multiplier because the multiplier is generally the slowest clement in the system. Furthermore, it is generally the most area consuming. Hence, optimizing the speed and area of the multiplier is a major design issue. However, area and speed are usually conflicting constraints so that improving speed results mostly in larger areas. As a result, a whole spectrum of multipliers with different area-speed constraints have been designed with fully parallel. Multipliers at one end of the spectrum and fully serial multipliers at the other end. In between are digit serial multipliers where single digits consisting of several bits are operated on. These multipliers have moderate performance in both speed and area. However, existing digit serial multipliers have been Plagued by complicated switching systems and/or irregularities in design. Radix 2^n multipliers which operate on digits in a parallel fashion instead of bits bring the pipelining to the digit level and avoid most of‘the above problems. They were introduced by M. K. Ibrahim in 1993. These structures are iterative and modular. The pipelining done at the digit level brings the benefit of constant operation speed irrespective of the size of’ the multiplier. The clock speed is only determined by the digit size which is already fixed before the design is implemented.


3.1. Basic binary multiplier

The operation of multiplication is rather simple in digital electronics. It has its origin from the classical algorithm for the product of two binary numbers. This algorithm uses addition and shift left operations to calculate the product of two numbers.

3.2. Partial product generation

Partial product generation is the very first step in binary multiplier. These are the intermediate terms which are generated based on the value of multiplier. If the multiplier bit is ‘0’, then partial product row is also zero, and if it is ‘1’, then the multiplicand is copied as it is. From the 2nd bit multiplication onwards, each partial product row is shifted one unit to the left as shown in the above mentioned example. In signed multiplication, the sign bit is also extended to the left.

Type Of Adders

In electronics, an adder is a digital circuit that performs addition of numbers. In modern computers adders reside in the arithmetic logic unit (ALU) where other operations are performed. Although adders can be constructed for many numerical representations, such as Binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement is being used to represent negative numbers it is trivial to modify an adder into an adder-subtracter

Types of adders

For single bit adders, there are two general types.

A half adder has two inputs, generally labeled A and B, and two outputs, the sum S and carry C. S is the two-bit XOR of A and B, and C is the AND of A and B. Essentially the output of a half adder is the sum of two one-bit numbers, with C being the most significant of these two outputs.

Multiplier types

Multipliers are categorized relative to their applications, architecture and the way the partial products are produced and summed up. Based on all these, a designer might find following types of multipliers.

5.1. Array multipliers

In array multipliers, the counters and compressors are connected in a serial fashion for all bit slices of the Partial Product parallelogram. As can be seen in Figure 21, the array topology is a two-dimensional structure that fits nicely on the VLSI planar process

5.2. Simple array multiplier

In this type of array, the output of each row of counters (3:2 compressors) is the input to the next row of counters [2]. In the simple array, each row of [3:2] compressors adds a partial product to the partial sum, generating a new partial
sum and a sequence of carries. The delay of the array depends on the depth of the array. Therefore, the summing time for the simple array is N-2 [3:2] compressor delays, where N is the number of partial products.
The drawback of this type of array is the hardware is underutilized. The counters are used only once in the calculation of the result, for the remaining time, they are idle. This drawback can be diminished by pipelining the array so that several multiplications can occur simultaneously.Pipelining would increase the throughput of the multiplier, but would also increase the latency and area of the multiplier. A fully pipelined array is normally avoided, since the array would be faster than the clock of processor. Figure 4.2.1 depicts the layout of a simple array topology. The dots represent the partial products.

5.3.Serial/Parallel Multiplier

In a serial/parallel multiplier,the multiplicand x arrives bit serially while the multiplier a is applied in a bit parallel format.A common approach used in such multipliers is to generate a row or diagonal of bit products in each time lot and perform the additions concurrently.

5.5.Shift-and-Add Multiplier
Shift-and-add multiplication is similar to the multiplication performed by pa-per and pencil. This method adds the multiplicand X to itself Y times, where Y de-notes the multiplier. To multiply two numbers by paper and pencil, the algorithm is to take the digits of the multiplier one at a time from right to left, multiplying the multi-plicand by a single digit of the multiplier and placing the intermediate product in the appropriate positions to the left of the earlier results.As an example, consider the multiplication of two unsigned 4-bit numbers, 8 (1000) and 9 (1001).

In the case of binary multiplication, since the digits are 0 and 1, each step of the multiplication is simple. If the multiplier digit is 1, a copy of the multiplicand (1  multiplicand) is placed in the proper positions; if the multiplier digit is 0, a number o 0 digits (0  multiplicand) are placed in the proper positions.

Consider the multiplication of positive numbers. The first version of the multiplier circuit, which implements the shift-and-add multiplication method for two n-bit numbers.


Many applications demand high throughput and real-time response, performance constraints that often dictate unique architectures with high levels of concurrency. DSP designers need the capability to manipulate and evaluate complex algorithms to extract the necessary level of concurrency. Performance constraints can also be addressed by applying alternative technologies. A change at the implementation level of design by the insertion of a new technology can often make viable an existing marginal algorithm or

The VHDL language supports these modeling needs at the algorithm or behavioral level, and at the implementation or structural level. It provides a versatile set of description facilities to model DSP circuits from the system level to the gate level. Recently, we have also noticed efforts to include circuit-level modeling in VHDL. At the system level we can build behavioral models to describe algorithms and architectures. We would use concurrent processes with constructs common to many high-level languages, such as if, case, loop, wait, and assert statements. VHDL also includes user-defined types, functions, procedures, and packages." In many respects VHDL is a very powerful, high-level, concurrent programming language. At the implementation level we can build structural models using component instantiation statements that connect and invoke subcomponents. The VHDL generate statement provides ease of block replication and control. A dataflow level of description offers a combination of the behavioral and structural levels of description. VHDL lets us use all three levels to describe a single component. Most importantly, the standardization of VHDL has spurred the development of model libraries and design and development tools at every level of abstraction. VHDL, as a consensus description language and design environment, offers design tool portability, easy technical exchange, and technology insertion

VHDL: The language

An entity declaration, or entity, combined with architecture or body constitutes a VHDL model. VHDL calls the entity-architecture pair a design entity. By describing alternative architectures for an entity, we can configure a VHDL model for a specific level of investigation. The entity contains the interface description common to the alternative architectures. It communicates with other entities and the environment through ports and generics. Generic information particularizes an entity by specifying environment
constants such as register size or delay value.


Our project and implimentation gives a clear concept of different multiplier and their implementation in tap delay FIR filter. We found that the parallel multipliers are much option than the serial multiplier. We concluded this from the result of power consumption and the total area. In case of parallel multipliers, the total area is much less than that of serial multipliers. Hence the power consumption is also less. This is clearly depicted in our results. This
speeds up the calculation and makes the system faster.

While comparing the radix 2 and the radix 4 booth multipliers we found that radix 4 consumes lesser power than that of radix 2. This is because it uses almost half number of
iteration and adders when compared to radix 2.

When all the threse multipliers were compared we found that array multipliers are most power consuming and have the maximum area. This is because it uses a large number of adders. As a result it slows down the system because now the system has to do a lot of calculation.

Multipliers are one the most important component of many systems. So we always need to find a better solution in case of multipliers. Our multipliers should always consume less power and cover less power. So through our project and implimentation we try to determine which of the these algorithms works the best. In the end we determine that radix 4 modified booth algorithm works the best.

prasenjit karmakar
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18-03-2011, 02:50 PM

hi,i need the verilog coding for the booth's multiplier for multipliying two 4 bit numbers.please send this........
seminar paper
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29-02-2012, 09:55 AM

to get information about the topic partial products designing low power multiplier full report ppt and related topic refer the link bellow





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