Description

Abstract

A new architecture, namely, Multiplier-and accumulator (MAC) based Radix-4 Booth Multiplication Algorithm for high-speed arithmetic logics have been proposed and implemented on Spartan6 FPGA project Board . By combining multiplication with accumulation and devising a hybrid type adder the performance was improved. The modified booth encoder will reduce the number of partial products generated by a factor of 2. Fast multipliers are essential parts of digital signal processing systems. The speed of multiply operation is of great importance in digital signal processing as well as in the general purpose processors. The number to be added is the multiplicand, the number of times that it is added is the multiplier, and the result is the product. Each step of addition generates a partial product.

Demonstration video

Tool required

Software:

• Xilinx ISE 14.7i

Language:

• VHDL

Hardware:

• Spartan6 FPGA project Board

Block Diagram for Implementation of Booth Multiplier

 

Introduction:

Booth Algorithm

Booth algorithm requires examination of the multiplier bits, and shifting of the partial product. Prior to the shifting, the multiplicand may be added to partial product, subtracted from the partial product, or left unchanged according to the following rules:

Look at the first least significant bits of the multiplier “X”, and the previous least Significant bits of the multiplier “X – 1”.

⇛0 0 Shift only

⇛1 1 Shift only.

⇛0 1 Add Y to U, and shift

⇛1 0 Subtract Y from U, and shift or add (-Y) to U and shift

⇛Take U & V together and shift arithmetic right shift which preserves the sign bit of 2’s complement number. Thus a positive number remains positive, and a negative number remains negative.

⇛Shift X circular right shift because this will prevent us from using two registers for the X value.

Booth Multiplier Output Image

 

 

 

 

Conclusion

Radix 4 modified booth algorithm was successfully implemented in Spartan-6 FPGA and output verified with switches and LED’s of Spartan6 FPGA project Board .

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