What Influenced The Use Of Binary Number System As The Basis Of Computer Language?

We use the binary number system in computer hardware because transistors (the building blocks of a computer) are only reliable at indicating a state of 'on' or 'off' - states of 1 and 0.  Hence the binary, base-2, number system is the way that all modern computers do their arithmetic and processing.

Since binary is quite a tedious system for humans to read, hexadecimal (base-16, easily mappable to and from base-2) is the de facto system for interpreting computer-related dimensions such as address space.