🚀 go-pugleaf

In article <76700180@p.cs.uiuc.edu>, gillies@p.cs.uiuc.edu writes:
> 
> nEven today, maybe we don't know the full intellectual costs of using
> binary numbers in computers.  I imagine Von Neumann weighed the
> technical advantages, and ignored the human factors.  I imagine he &
> his group did not forsee these costs:
> 
> (1) Professional programmers must be fluent in 3-4 bases
>     (binary, octal/hex, decimal), boolean logic, and arithmetic systems
>     (sign-magnitude, one's complement, two's complement).  This is no
>     trouble to Von Neumann, but try to teach most high-school kids this.

I would rather try to teach this to elementary school kids than to 
programmers.  It is trivial compared to the programming languages.

> (2) Numerical algorithms must deal with binary roundoff.

I can see no way that binary roundoff is any worse than decimal roundoff.
It is usually a lot better.  Besides, factors of 2 and 4 are very common
in numerical procedures, and factors of 10 are rare.  Also, such common
functions as square root and the elementary transcendental functions are
easier to deal with in binary.  The CORDIC algorithms are much easier in
binary than decimal.

> (3) Accounting algorithms must hassle with representing .1 in binary

There are many ways around this problem.  Even accounting roundoff is
binary.

> (4) The industry struggled for years with 6/7-bit characters (too
>     little), and finally settled on 8-bit characters (too much).  
>     In decimal, 2-digit characters would have made sense on day 1.

Are 8-bit characters too much?  Unless someone is willing to use the
usual typewriter characters only, 8 bits are too little.

> (5) The necessity to learn / program conversion algorithms.

A.  It is easy.

B.  It is no more necessary for the programmer to learn than to learn to
program elementary transcendental functions.

> Can anyone think of other human costs of binary numbers?

Other than making humans think occasionally, no.  But there are many costs
of not using binary numbers.  Bit vectors are extremely useful, as are other
binary devices which I suspect many programmers and programming gurus are
not aware of.  I know of far too many uses of binary arithmetic.  In fact,
I would prefer to have more use of binary; I find the use of decimal numbers
for register designations very annoying, and even the default that numbers
are decimal, expecially floating point, a hindrance to efficient coding.

Why is it necessary to design computers (and anything else) so that they
cannot be used efficiently by those capable of arising above the trivial?
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)