#### 1. How to convert binary to decimal ?

1. Find the position of every binary digit. We should count the position from the right direction of the number. And the position count starts from 0.

#### Example

**0001** - position of 1 = 0, 0 = 1, 0 = 2, 0 = 3.

2. Multiply every digit with 2 to the power of their corresponding position. (2 ^{position})

3. Finally, calculate the sum of all the multiples.

_{2}to decimal

= 1 x 2 ^{3} + 1 x 2 ^{2} + 1 x 2 ^{1} + 1 x 2 ^{0}

= 8 + 4 + 2 + 1

= (15)_{10}

_{2}to decimal

= 1 x 2 ^{3} + 0 x 2 ^{2} + 0 x 2 ^{1} + 1 x 2 ^{0}

= 8 + 0 + 0 + 1

= (9)_{10}

#### 2. How to convert binary to octal ?

Group every 3 binary bits from right to left and construct the octal number system.

_{2}to octal

= (101010101)_{2}

= (101)(010)(101)

= (525)_{8}

_{2}to octal

= (11111111)_{2}

= (11)(111)(111)

= (377)_{8}

#### 3. How to convert binary to hexadecimal ?

Group every 4 binary bits from right to left and construct the hexadecimal number system.

_{2}to hexadecimal

= (101010101)_{2}

= (1)(0101)(0101)

= (155)_{16}

_{2}to hexadecimal

= (11111111)_{2}

= (1111)(1111)

= (15)(15)

= (ff)_{16}

__Converting Decimal Fraction to Binary, Octal, Hexadecimal __

A fractional number is a number less than 1. It
may be .5, .00453, .564, etc. We use the multiplication operation to
convert decimal fraction to any other base.

**To convert a decimal fraction to—**

**• binary **- multiply by 2

**• octal **- multiply by 8

**• hexadecimal** - multiply by 16

#### Steps for conversion of a decimal fraction to any other base are—__ __

1. Multiply the fractional number with the to Base, to get a resulting number.

2. The resulting number has two parts, non-fractional part and fractional part.

3. Record the non-fractional part of the resulting number.

4. Repeat the above steps at least four times.

5. Write the digits in the non-fractional part starting from upwards to downwards.

#### Example-1: Convert 0.2345 from Base 10 to Base 2

The binary equivalent of (0.2345)_{10} is (0.001111)_{2}

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