Why is two to the power of zero equal to binary one? Probably a simple question and possibly not asked very well. What I want to know is..
In binary, a decimal value of 1 is also 1.
It can be expressed as  $x = 1 \times 2^0$
Question:
Why is two to the power of zero equal to one?
I get that two to the power of one is equal to two, or binary 10, but why is to the power of zero equal to one, is this a math convention? is there a link I could read?

The definition $\ 2^0 = 1\ $ is "natural" since it makes the arithmetic of exponents have the same structure as $\mathbb N$ (or $\mathbb Z\:$ if you extend to negative exponents). In more algebraic language: the definition is the canonical extension of the powering homomorphism from $\rm\ \mathbb N_+\: $ to $\rm \mathbb N\ $ (or $\rm\: \mathbb Z\:$),$\ $ viz. $\rm\ 2^n\ =\ 2^{n+0}\ =\ 2^n\ 2^0\ $ $\rm\Rightarrow\ 2^0 = 1\:$. It's just a special case of the fact that the identity element must be preserved by structure preserving maps of certain multiplicative structures (e.g. commutative cancellative monoids).
It may be viewed as a special case of adjoining an identity element to a commutative semigroup. And it proves very convenient to do so, for the same reason it proves convenient to adjoin the identity element 0 to the positive natural numbers, e.g. it allows every element to be viewed as a sum, so one can write general formulas for sums that work even in extremal cases where an element is indecomposable (e.g. by writing $ 1 = 1 + 0 $ vs. having to separate a special case for the sum-indecomposable element $1$ or, in $\,2^{\Bbb N},\,$ for  $\, 2 = 2\cdot 1 $). Empty sums and products prove quite handy for naturally founding inductions and terminating recursive definitions.
