Binary Decimal and Hexadecimal converter

Conversion from Decimal:

For example let's convert decimal 59 to Binary and Hexadecimal format.

To Binary:

Division by base of binary ( 2)	Reminder
59 / 2 = 29	1
29 / 2 = 14	1
14 / 2 = 7	0
7 / 2 = 3	1
3 / 2 = 1	1
1 is not divisible by 2	1

Now writing the reminder from bottom to top will give the binary equivalent of 59 which is 11011

To Hexadecimal

Divide by base of Hexadecimal ( 16 )	Reminder in decimal	Reminder in Hex
59 / 16 = 3	11	B  ( Equivalent hex value for 11, check the below table )
3 is not divisible by 16	3	3

Writing the reminder values in Hex from bottom to top gives the Hex equivalent value for 59 which is 3B.

Here is the list equivalent Hex value for decimal values

Decimal	Hex
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	A
11	B
12	C
13	D
14	E
15	F

Conversion from Binary:

Now let's see how binary number of 111011 is converted to Decimal and Hexadecimal

To Decimal:

To convert to decimal we need to multiply each of the binary digits with 2ⁿ where n is the position of the binary digit in the number

111011 = ( 1 x 2⁵ ) + ( 1 x 2⁴ ) + ( 1 x 2³ ) + ( 0 x 2² ) + ( 1 x 2¹ ) + ( 1 x 2⁰ )

= ( 1 x 32 ) + ( 1 x 16 ) + ( 1 x 8 ) + ( 0 x 4 ) + ( 1 x 2 ) + ( 1 x 1 )

= 32 + 16 + 8 + 0 + 2 + 1

= 59₁₀

To Hexadecimal

To convert Hex number to Binary, convert them to decimal first and then make the conversion from decimal to Hex value.

Conversion from Hexadecimal:

Let's convert the hex number to 3B to decimal and binary format.

To Decimal:

Conversion from Hex can be done by multiplying each of the hex digits with 16ⁿ where n is the position of the hex digit in the number

3B = 3 x 16¹ + B x 16⁰

= 3 x 16 + 11 x 1

= 48 + 11

= 59₁₀

To Binary:

To convert a hex value to binary, first convert the value to decimal and then convert it from decimal to Binary using the methods shown above.