# 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.

#### Convert (1111)_{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}

#### Convert (1001)_{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.

#### (101010101)_{2} to octal

= (101010101)_{2}

= (101)(010)(101)

= (525)_{8}

#### (11111111)_{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.

#### (101010101)_{2} to hexadecimal

= (101010101)_{2}

= (1)(0101)(0101)

= (155)_{16}

#### (11111111)_{2} to hexadecimal

= (11111111)_{2}

= (1111)(1111)

= (15)(15)

= (ff)_{16}

15 equivalent hexadecimal value is **f**.