Why binary numbers are used?
It may be observed from the discussions of the preceding section that the use of a base smaller than 10 requires more positions to represent a given decimal number. As for example, the binary number 10101 requires 5 bit positions to represent the decimal number 21 which requires two positions for its decimal representation. This is a major disadvantage of the binary number system. In spite of this fact, all the modern digital computers have been basically designed on the basis of binary number system.
Why this bias to binary number?
There are several reasons for this.
The first and foremost reason is that electronic components, as a natural coincidence, operate in a binary mode. A switch is either open/off (called 0 state) or closed/on (called 1 state); a transistor is either not conducting (0 state) or is conducting (1 state).
This two-state nature of the electronic components can be easily expresses with the help of binary numbers.
The second reason is that computer circuits have to handle only two bits instead of 10 digits of the decimal system. This simplifies the design of the machine, reduces the cost and improves the reliability.
Lastly, binary number system is used because all the operations that can be done in the decimal system can also be done with a binary number of radix 2.