# -10^2 (OT)

Raymond E. Griffith rgriffit at ctc.net
Tue May 27 21:39:00 EDT 2003

```on 5/22/03 1:51 PM, Dar Scott at dsc at swcp.com wrote:

>
> On Thursday, May 22, 2003, at 11:32 AM, David Squance wrote:
>
>> -10*-10 is ambiguous, since you have two operations adjacent to each
>> other
>> (ultra picky, I know)
>> Assuming *-10 is meant to be *(-10), -10*-10 = -(-100) = 100
>
> I'm having trouble seeing an alternate meaning.
>
> Dar
>

Here is the issue:

Remember that numbers represented in computers are not represented in
decimal form, but in a binary form. Negative numbers are not represented
with a negative sign, but rather as a binary with a different first digit (1

The algebraic order of operations is
Parentheses, Exponent, Multiplication and Division (from left to right), and
Addition and Subtraction (from left to right), or PEMDAS

But algebraically, negation is a multiplication process. -5 = -1*5. So
-10^2 means -1*10^2, or -100.

Algebraically, the exponent only affects what it touches. That is why -10^2
means -1*10^2, and not (-10)^2.

But since computers see numerical representation differently, the negation
of a number is not a real "operation" to a computer. -10 is a single unit.
So -10^2 in computer languages will always mean (-10)^2.

Anti-intuitive? Yup. But if the engine were rewritten to check and correct
for this algebraically, it would run a lot slower. Better for us just to
recognize the difficulty and code around it.

Raymond E. Griffith

```