Because CPUs (heart of computer) main part consists of triggers - electronic devices that can be in one of two possible states: charged, discharged. So, one trigger can store one binary digit. Combining triggers in rows we can store big binary digits. Adding combinational logic we can perform basic ariphmetics.
Because the earliest computers were simply banks of switches. Switches normally only have two positions - on & off. This is represented in binary as 1 or 0 (one or zero). Even in today's ultra-modern computers, inside the micro-chips, the same situation applies - lots of microscopic switches moving at ultra-fast speed.
The circuitry that makes up the inner workings of a computer comes from transistor type circuits. The transistor circuits are configured to have only two states. This could be measured as a voltage (for example the output voltage is either 5 volts or zero volts). Therefore each state is represented by a one(1) or zero(0). Normally, if there is voltage present, then the value is 1, and zero voltage present, then it is a 0. I gave an answer very similar to this one for another question asking about Boolean algebra and computers
They use the binary code (1010101011001100)
The first computer to use the binary number system was probably the Z1, started by Konrad Zuse in 1936. It was a mechanical computer, not fully programmable, but is still considered a computer.
Binary
Binary Number System
Computers are based on a binary number system.
It is known as the binary code.
Binary number system ,which has only two digits 0 and 1.
binary data
on the computer
Binary-
the binary numeral system
0 and 1.