CZ1101, Lab 3, Week 10, 15 - 20 Sept. Due Tuesday, 23 September, 1997

Submit your assembly program, and report your test outputs by the due date.

  1. Write a procedure, booth, in MIPS assembly language. The booth procedure implements Booth's algorithm in software for signed multiplication of two's complement numbers, using only addition, subtraction, and logical operations. See textbook or lecture notes for detail on Booth's algorithm.

    The procedure booth takes three arguments, in $4, $5, and $6; $4 contains a 32-bit multiplicand, $5 contains a 32-bit multiplier, the result should be stored at an address in $6. Since the result is a 64-bit number, two words are needed. Let us agree that we store the lower 32-bit of the result in location 0($6), and the upper 32-bit of the result in 4($6). Since the product of two 32-bit numbers is 64 bits, it is necessary to use two 32-bit registers together as a single 64-bit register for the product P.

    The values in $4, $5, and $6 are not set in your procedure but are passed from the calling program, i.e., from the main. You should assume that the registers have already had proper values.

    A procedure is similar to a function in C that can be called multiple number of times. The main program gives you an example of procedure call in MIPS assembly language. You can down load the program from our web page HERE.

    Test your program with the following set of data:

       0 x 1, 
       2 x (-1), 
       5 x 3,
       (-2^{16}) x 2^{16},
       (2^{31} - 1) x (2^{31} - 1),
       (-120909809) x (-907129051).
    Make sure that the answers for all cases are what you expected. Report your results (products) as 16 hexadecimal digits.

Further remarks from Shing Gene and Dr. Wang.