Homework Assignment 8

                    Advanced Computer Architecture
                               CS 350c

                         Unique Number: 51160
                             Spring, 2016

                        Given:  March 8, 2016
                         Due:  March 24, 2016



This homework concerns improving your knowledge of combinational
logic.

 1.  Of the 16 possible, what 2-input logical connectives (such as
     AND, OR) that are complete?  That is, what 2-input
     connectives can be used to implement all of the other 15
     connectives?

 2.  In terms of 2-input logical connectives, what is the equation (in
     C-language code) for a three-input majority circuit?  Please
     write your answer as a C-language function.  Thus, define the
     function like this:

     int three_bit_majority( int x, int y, int z ) {
       int x_and_y = x & y;
       ...
       return ( ans );
     }

     where integers x, y, z, have as input either 0 or 1, and fill in
     the body.

The rest of this homework are to be defined in terms of 2-input
logical connectives, where each input is a single bit.

 3.  Write down the equation (in C-language code) for a 4-bit adder.
     Write a structure definition to return four bits, a carry bit,
     and an overflow bit.  This definition should be implemented as a
     ripple-carry adder.

 4.  Write down the equation (in C-language code) for a 4-bit adder
     that has a carry-save implementation.  Use the structure defined
     for problem 3 (just above) to return the result.

 5.  Write down the equation for a 4-bit multiplier that expected 4-bit
     signed numbers and produces a correct 8-bit signed answer.

For problems 2 through 5, be sure to run your solutions through the
C-compiler and exhaustively test them.

 6.  Write down the equation for a 32-bit adder (any implementation
     will do).  Can you test it?