# 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: - 17/2 = 8 + ½

a0 = LSB = 1

Step2: - 8/2 = 4 + 0

a1 = left bit to LSB (a0) = 0

Step3:- 4/2 = 2 + 0

a2 = left bit to a1 = 0

Step4:- 2/2 = 1 + 0

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:- 0.25*2 = 0.50 + 0

b0 = 0

Step7:- 0.50*2 = 0.00 + 1

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)

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#### Binary to Decimal conversions:

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

Example: Convert 101010.1 to decimal

The equivalent decimal value

= 1*(2^5) + 0*(2^4) + 1*(2^3) + 0*(2^2) + 1*(2^1) + 0*(2^0) + 1*(2^-(1))

= 32 + 0 + 8 + 0 + 2 + 0 + 0.5

= 42.5

Answer. The decimal equivalent of (101010.1) is 42.5

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