LAB 3

Due Friday, October 15, 5PM

Negabinary Arithmetic Program

Base -2 is one of my favorites!  As with any other bases, the
weight of position i is b^i, so the positions for an 8-bit negabinary
number are:
   ...  -128 64 -32 16 -8 4 -2 1  . -(1/2) 1/4 -(1/8) ...

In our binary 32-bit MIPS world, the easiest thing to do on input is
to separate the positive and negative parts (using a masking logical
operation) and subtract them to get an internal 2s complement
representation. 

To output a negabinary number, we can use a divide by -2 algorithm,
but with adjustments to ensure that the remainder is either 0 or 1
(ie, never -1):

-----------------------------------------
 37/ -2 = -18 r 1 
-18/ -2 =   9 r 0
  9/ -2 =  -4 r 1 
 -4/ -2 =   2 r 0
  2/ -2 =  -1 r 0
 -1/ -2 =   0 r -1  => -1 r 1
  1/ -2 =   0 r 1

 64  -32  16 -8 4 -2 1
  1    1   0  0 1 0 1	

  37 = 1100101
-----------------------------------------
  7/ -2 =  -3 r 1
 -3/ -2 =   1 r -1 => 2 r 1
  2/ -2 =  -1 r 0
 -1/ -2 =   0 r -1 => 1 r 1
  1/ -2 =   0 r 1

 16 -8 4 -2 1
  1  1 0  1 1

  7 = 11011
-----------------------------------------

Division by 2 in signed integers corresponds to rightshift with some
corrections, so you can examine the bottom bit and use knowledge of
the bottom bit and the iteration number (ie, even or odd (= pos or neg
bit position) to determine the next dividend and the next bit.


Write a program to convert between the following formats with input
format specified by user.

Formats:  (u) unsigned binary
	  (s) sign/mag binary
	  (1) 1s complement
	  (2) 2s complement
	  (n) negabinary
	  (d) decimal integer

Use getc and putc for all the [nega]binary bases.
Use geti and puti for integers.

Example:

	<helpful help message and greeting>

<Enter number of bits for output>: 8
<Enter input format and number>: n1010
<print out 1010 (base -2) in the other formats>

=============================================================
You may want to talk to TAs and classmates  about the algorithms
needed for this at the C level, or the use of specific instructions in
MAL examples unrelated to this problem.  Feel free to post negabinary
conversions on the newsgroup to see if they're correct.  Similarly,
feel free to post questions about MAL syntax like how to print a
string, and the like.

SUBMIT:  nega.mal
	 README
	     a.  Name and email address
	     b.  Overview of your code
	     c.  Thoughts on negabinary -- 
		 -- What is the range of an n-bit negabinary number?
		 -- How would you add 2 negabinary numbers?
		 -- In what circumstances might negabinary be useful?
             d.  Any other comments on MAL.

Things to help get a +:
       - great prompts, error messages and the like
       - inclusion of excess notation with user-entered excess

Things to that may lead to a - (but still credit):
       - Everything but the negabinary output
       - Can only handle 8-bit numbers
         (+ items may help move either of these to a check.)

Revision:
    Submit 5:00 pm 10/18 program for any 1 non-decimal input to any 1
    non-decimal output.

    Submit 5:00 pm on 10/22 the complete program.