On Thu, 13 Mar 2003 at 23:55:51, P Witte wrote:
(ref: <[EMAIL PROTECTED]>)
>
>Tony Firshman writes:
>
>>>Monetary calculations normally only require the four basic
>>>operations, add, subtract, multiply and divide.
>
>>Surely two only - addition and subtraction?
>>Multiplication and division are shorthand for
>>addition/subtraction in my book.
>>
>>... or am I being too simplistic.
>
>It all depends on what youre trying to do. Working out percentages requires
>the use of multiplication and division, for example, and as someone pointed
>out, you'll need powers to calculate compound interest rates. Theres no
>limit. Look at large companies, such as the late Enron, they even use
>imaginary numbers! However, nowadays, subtraction seems to be all the rage.
>
>As you point out in a later mail, most of these operations are merely
>addition or subtraction at heart.
Exactly. Everything is addition (incl sign changes) - it is just too
tortuous.
> I once had an old mechanical calculating
>machine, given to me by my grandfather to play with when the bank he worked
>for upgraded to electro-mechanical ones. I later used it for my homework,
>the only kid at school with access to a calculator, (something I had to keep
>secret as my teacher would not have approved.) Division was quite a
>convoluted affair involving multiple subtractions and shifts. I used that
>same algorithm later in my assembler longword division routine.
I am your grandfather it seems, as these were, other than slide rules,
the only mechanical things we had at Imperial College in the 60s.
Even transistors were new then (8-)#
Was yours the one you had to turn a handle - one way for addition and
the other for subtraction, and shift manually?
Using methods like that, as you say, give one a good feel for the
mechanics of programming.
The same could be said for the UK101 (almost all discrete 74X TTLs) and
computer hardware.
Sinclair ULAs don't give any good feel of what the poor old computer is
actually _doing_ at the basic level.
Even the system clock on the UK101 was divided by 7404s!
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