[Solved] Digital_ IC Homework 2- Booth Algorithm

1. Introduction:

Booth algorithm is a multiplication operation that multiplies two numbers in twos complement notation. The detail algorithm is described as below:

• Assume that the multiplicand m is x-bit and multiplier r is y-bit.

Initialize a register P for the final result, and the length is x+y+1 bits.

The initial value of P is 0(x bits)_r(y bits)_0(1 bit).

• The rightmost 2 bits used for the selection of different executions.

* Overflow condition can be ignored during the execution.

• Arithmetically shift 1 bit on P.
• Repeat the step (2) and (3) for y times.
• The final answer is obtained by dropping the LSB from P.

2. Design Specifications:
   • Block Overview

Fig. 1. The block overview.

• I/O Interface

• File Description

3. Scoring:
   • Functional Simulation [60%]

All of the result should be generated correctly, and you will get the following message in ModelSim simulation.

Fig. 2. Functional simulation result.

• Gate-Level Simulation [30%]
  • Synthesis

Your code should be synthesizable. After it is synthesized in Quartus, a file named booth.vo will be obtained.

• Simulation

All of the result should be generated correctly using booth.vo, and you will get the following message in ModelSim simulation.

Fig. 3. Gate-level simulation result.

DeviceCyclone II EP2C70F896C8

• Performance [10%]

The performance is scored by the clock width your design can operate in gatelevel simulation. The score will be decided by your ranking in all received homework. (The smaller the better)