Binary Number System

1. Most modern computer systems operate using the binary logic. A computer cannot operate on the decimal number system.

2. A binary number system uses only two digits namely 0 and 1.

3. The binary number system works like the decimal number system except one change. It uses the base 2.

4. Hence the largest value of a digit is 1 and the number values a digit can assume is two i.e. 0 and 1.

5. The weighted values for different positions for a binary system are as shown in figure below:

6. The binary digits (0 and 1) are also called as bits. Thus binary system is a two bit system.

7. The leftmost bit in a given binary number with the highest weight is called as Most Significant Bit (MSB) whereas the rightmost bit in a given number with the lowest weight is called as Least Significant Bit (LSB).

Example: Express the binary number 1011.011 in terms of powers of 2.

Solution: The required representation is shown below:

• 1011.011 = 1*2³ + 0*2² + 1*2¹ + 1*2⁰ + 0*2^-1 + 1*2^-2 + 1*2^-3

Applications of Binary Number System

The implementation of binary number system in digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers and computer-based devices such as mobile phones. Each digit is referred to as a bit.

Advantages of Binary Number System

1. Easily implementation in an electronic system by using on/off signals and nothing in between. 
2. On/off signal's provide very reliable operation. Extremely low possibility of errors when transferring data because it is easy to decide the difference between the on and off state of the circuit and some noise or disruption during the transfer process will not disrupt that decision.

Disadvantages of the Binary Number System

1. The binary number system has an important drawback. It requires a very long string of 1's and 0's to represent a decimal number. For example; (128) = (10000000)
2. So we require 8 bits to represent (128). Imagine what will happen if (348678) is to be converted into binary number.
3. Every different type of data (e.g. words, numbers, images, music, speech, etc) must be converted to and from the binary representation for human use. 
4. The on/off nature of circuits using binary causes issues when trying to get high speed computation.