# Binary Numbers Discussion.

**Bit****:** The smallest unit of a digital `system`

is called a ‘bit’. A bit can take one of the two logical values of 1 or 0. A set of 4 bits can represent (=2^4) 16 decimal values. And a set of 5 bits can represent (=2^5) 32 decimal values... and so on.

**Byte:** All the discrete information in digital `system`

s is represented as group of bits. A similar group of 8 bits is called a byte.

Decimal to binary conversion:

Formula to convert a decimal number to binary: Is derived using an example below.

##### Decimal to binary conversion

Formula to `convert`

a decimal number to binary: Is derived using an example below.

Example: To represent 17.25 in digital `system`

we will need to use 5 bits.

**Step1**: -

a0 = LSB = 1

**Step2**: -

a1 = left bit to LSB (a0) = 0

**Step3**:-

a2 = left bit to a1 = 0

**Step4**:-

A3 = left bit to a2 = 0

**Step5**:-

A4 = left bit to a3 or most significant bit (MSB) = 1

The equivalent binary number for 17 decimal is = (a4a3a2a1a0) = (10001)

**Step6**:-

b0 = 0

**Step7**:-

b1 = 1

The equivalent binary number for 0.25 decimal is = (0.b0b1) = (0.01)

**Answer:** The equivalent binary number for **17.25** decimal = (a4a3a2a1a0.b0b1) = (10001.01)