Here we will discuss about the binary number system we already know binary numbers play a vital role in the design of digital computers.

Hence
a detailed discussion of binary number system is given in this section. Binary
number system uses two symbols 0 and 1 and its radix is 2. The symbols 0 and 1
are generally called **BITS** which is a
contraction of the two words Binary digits.

a

For fractional binary numbers, the base has negative integral powers starting with -1 for the bit position just after the binary point.

The bit at the extreme left of a binary number has the highest positional value and is usually called the **Most Significant Bit** or **MSB**. Similarly, the bit occupying the extreme right position of a given binary number has the least positional value and is referred to as the **Least Significant Bit** or **LSB**.

To facilitate the distinction between different number
systems, we generally use the respective radix as a subscript of the number.
However the subscript will not be used when there is no scope of confusion.

**In binary number system a few examples on binary numbers
and their decimal equivalents are given below:**

= 32 + 0 + 8 + 4 + 0 + 1

= 45

The above results can be more clearly expressed in the following manner:

** Binary point**

111.1011

= 1 × 2

= 4 + 2 + 1 + .5 + 0 + .125 + .0625

= 7.6875

**The above results can
be more clearly expressed in the following manner:**

These are the basic examples shown above.

- Why Binary Numbers are Used

- Binary to Decimal Conversion

- Conversion of Numbers

- Hexa-decimal Number System

- Conversion of Binary Numbers to Octal or Hexa-decimal Numbers

- Octal and Hexa-Decimal Numbers

- Signed-magnitude Representation

- Radix Complement

- Diminished Radix Complement

- Arithmetic Operations of Binary Numbers

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