Base 16 number system which consists numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f}.

#### Decimal Number System

Base 10 number system which consists numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

Decimal Number System

## Hexadecimal to Decimal Conversion Procedure

1. Write down the decimal equivalent of hexadecimal.

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

#### Example

1caf - position of f = 0, a = 1, c = 2, 1 = 3.

5afb - position of b = 0, f = 1, a = 2, 5 = 3.

3. Multiply every digit with 16 to the power of their corresponding position. (16 position)

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

Decimal

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9

10

A or a

11

B or b

12

C or c

13

D or d

14

E or e

15

F or f

## Example

#### (16)16 to decimal

position = {1-1, 6-0}

= 1 x 16 1 + 6 x 16 0

= 16 + 6

= (22)10

## Example

#### ffff to decimal

position = {f-3, f-2, f-1, f-0}

f equivalent decimal = 15

= 15 x 16 3 + 15 x 16 2 + 15 x 16 1+ 15 x 16 0

= 15 x 4096 + 15 x 256 + 15 x 16 + 15 x 1

= (65535)10

## Example

#### 16ab to decimal

position = {1-3, 6-2, a-1, b-0}

a equivalent decimal = 10

b equivalent decimal = 11

= 1 x 16 3 + 6 x 16 2 + a x 16 1+ b x 16 0

= 1 x 4096 + 6 x 256 + 10 x 16 + 11 x 1

= 4096+1536+160+11

= (5803)10

## Example

#### ab0cffcd to decimal

position = {a-7, b-6, 0-5, c-4, f-3, f-2, c-1, d-0}

a equivalent decimal = 10

b equivalent decimal = 11

c equivalent decimal = 12

d equivalent decimal = 13

f equivalent decimal = 15

= a x 16 7 + b x 16 6 + 0 x 16 5+ c x 16 4 + f x 16 3 + f x 16 2 + c x 16 1+ d x 16 0

= 10 x 268435456 + 11 x 16777216 + 0 x 1048576 + 12 x 65536 + 15 x 4096 + 15 x 256 + 12 x 16 + 13 x 1

= 2684354560+184549376+0+786432+61440+3840+192+13

= (2869755853)10