16-bit Booth-Multiplier-in-iverilog

Project Details

“16-bit Booth’s Multiplier”

III Sem, B.Tech. (CSE)

Aug-Dec ‘19 - Digital Design and Computer Organisation Laboratory

Coding language: iVerilog+GtkWave

Problem Description

Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation.

Implementation

Booth's algorithm can be implemented by repeatedly adding (with ordinary unsigned binary addition) one of two predetermined values S(sum of multiplicand and accumulator) and D(difference of multiplicand and accumulator) to a product P, then performing a rightward arithmetic shift on P.

Modules and sub-modules

1. booth_multiplier(): This module takes in two signed 8-bit inputs, the multiplicand and the multiplier, and generates one signed 16-bit output, the product. Inputs: two 8-bit signed binary numbers Outputs: one 16-bit signed binary number This module implements one sub-module: booth_substep().

2. booth_substep(): By considering the Q[0] and q0, this module performs one iteration of the Booth’s multiplication process. Inputs: 8-bit signed accumulator, 8-bit signed multiplier, 8-bit signed multiplicand, q0. Outputs: 8-bit signed next-value-of-accumulator, 8-bit signed next-value-of-multiplier, next_q0 This module implements one sub-module: eight_bit_adder_subtractor().

3. eight_bit_adder_subtractor(): Depending on cin (0 for add, 1 for sub), the two 8 bit numbers passed to it are either added or subtracted. Inputs: cin, 8-bit signed input ‘a’, 8-bit signed input’b’. Outputs: 8-bit signed output ‘sum’ This module implements two sub-modules: (defined in lib.v) a) xor2 (performs xor on two 1-bit inputs and results in one 1-bit output) b) fa (full-adder module for two 1-bit inputs and one carry-in input and results in one sum output and one carry-out output).

PES University, 2019.