> At 02:21 PM 4/12/2007, William Couture wrote:
>
>>What's worse, I've worked with a control systems engineer (Ph.D., no
>>less) who could not divide by 2 in his head...
>
> That's because he was having problems with the binary to decimal
> conversion (in his head) after first converting the decimal value to
> binary, then discarding the LSB.  <grin>
>
> dwayne
>

This reminds me, I recently bought a textbook on digital design using
VHDL. EVERY textbook I've seen says that to figure out the decimal
equivalent of a negative twos complement number, take the twos complement
(making it positive), convert to decimal, then add the minus sign.

Something I read in BYTE magazine MANY years ago, that I have not seen
published elsewhere, is, I think, much simpler.

When using twos complement, make the sign of the weight of the msb
negative. Then add up bits times weights, as usual.

For example, in an 8 bit number, the msb weight becomes -128 instead of
128. So, 10101010 is:

1*(-128)=-128
0*64=0
1*32=32
0*16=0
1*8=8
0*4=0
1*2=2
0*1=0

and -128+32+8+2=-86.

Doing it the "hard way," we do this:

10101010
01010101 - ones comp
01010110 - add one to get twos comp
64+16+4+2=86, but this is the opposite of our original number, so the
original number was -86.

In both cases, you have to add the product of bits and weights, but in the
first method you don't have to twos complement.

I always thought it was pretty clever...

Harold


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