MIPS Computer Organization Project 4 – Booth's Multiplication Solved

Computer Organization Project 4 –

Booth's Multiplication 

In this project, you are required to perform a complete run of Booth's algorithm on two 

16-bit signed numbers. The generation steps for the two numbers are described as follows. 

 

1-    Assume that the numerical part of your student ID is A. 

2-    The square of A is B (B = A2). Use binary representation to represent B. 

3-    Right shift B for 16 bits, take the lower 15 bits, and append an extra bit '0' to the most significant bit (MSB) to form a new 16-bit number C. (i.e., C is a positive number.) 

4-    Right shift B for 16 bits, take the lower 15 bits, and append an extra bit '1' to the most significant bit (MSB) to form a new 16-bit number D. (i.e., D is a negative number.) 

5-    Perform C×D by using the Booth's algorithm. 

 

Please submit your Booth's multiplication result according to the following rules: 

1-    You are required to write every detailed step according to our lecture notes. 

2-    Upload your homework in TEXT format. 

3-    The filename is your student ID (e.g., B12345678.txt). 

 

Example: 

 

A  = 12345678 

B  = 100010101001111100001111100011000011001111000100 

C  = 0000111110001100 

D  = 1000111110001100 

CD 

 

Step               Product                  Next 

0    0000000000000000 1000111110001100 0   00 - shift 

1    0000000000000000 0100011111000110 0   00 - shift 

2    0000000000000000 0010001111100011 0   10 - sub 

3    +1111000001110100 

       1111000001110100 0010001111100011 0 

       1111100000111010 0001000111110001 1   11 - shift 

                       … 

14     0000001111000110 1101001001000010 0   00 - shift 

15     0000000111100011 0110100100100001 0   10 - sub 

16     +1111000001110100 

       1111001001010111 0110100100100001 0 

       1111100100101011 1011010010010000 1   done 

 CD = 1111100100101011 1011010010010000