Hexadecimal to Decimal
Converter

How to convert hexadecimal to decimal

To convert a hexadecimal number (base-16) to the decimal (base-10) number system, we need to use hexadecimal place value to add the base-16 value of each digit.

In the hexadecimal place value system, each time you move a place to the left, the value increases by a factor of 16.

In hexadecimal, the digit values go from zero to 15, with the letters A, B, C, D, E and F representing the numbers 10, 11, 12, 13, 14 and 15 respectively.

This table above shows the number 4C50E in the hexadecimal number system.

We can also write this as (4C50E)₁₆.

1) Convert 2c7 from hexadecimal to decimal.

Step 1) Write down the place value of each digit.

Step 2) Add up the place value of each digit.

(2 x 256) + (12 x 16) + (7 x 1)

= 512 + 192 + 7 = 711

So 2c7 in hexadecimal is equal to 711 in decimal.

Or we could say (2c7)₁₆ = (711)₁₀

2) Convert 1a7d from hexadecimal into decimal.

Step 1) Write down the place value of each digit.

Step 2) Add up the place value of each digit.

(1 x 4096) + (10 x 256) + (7 x 16) + (13 x 1)

4096 + 2,560 + 112 + 13 = 6781

So 1a7d in hexadecimal is equal to 6781.

Or we could say (1a7d)₁₆ = (6781)₁₀

How to convert from decimal to hexadecimal

To convert a decimal number (base-10) to the hexadecimal (base-16) number system, we need to change the decimal base-10 place value into hexadecimal base-16 place value.

We can do this in different ways by using division and looking at quotients and remainders.

The best way to see this is to look at some worked examples .

Example 1) Convert 330 from decimal to hexadecimal.

Step 1) Look at what hexadecimal place values we need.

The powers of 16 are 1, 16, 256, 4096, 65536, ...

Our value is just 330, so the powers of 16 we need are 1, 16 and 256 (up to 16²).

Step 2) Divide 330 by the highest place value number.

So we now divide 330 by 256 = 1 r. 74

The quotient tells us what number goes into with the place value of 256, which is 1.

Step 3) We now divide the remainder by the next (lower) power of 16.

So we have 74 ÷ 16 = 4 r. 10

The quotient us what number goes with the place value of 16, which is 4.

Step 4) Divide the remainder by the next (lower) power of 16.

So we have 10 ÷ 1 = 10 (which is A in hexadecimal)

This tells us which number goes with the place value of 1s which is A.

Step 5) Put your place value parts together.

Our number 330 = (1 x 256) + (4 x 16) + (10 x 1).

So our hexadecimal answer is 14A.

Or we could say that (330)₁₀ = (14A)₁₆

Example 2) Convert 8637 from decimal to hexadecimal.

Step 1) Look at what hexadecimal place values we need.

The powers of 16 are 1, 16, 256, 4096, 65536, ...

Our value is 8637, so the powers of 16 we need are 1, 16, 256 and 4096(up to 16³).

Step 2) Divide 8637 by the highest place value number.

So we now divide 8637 by 4096 = 2 r. 445

The quotient tells us what number goes into with the place value of 4096, which is 2.

Step 3) We now divide the remainder by the next (lower) power of 16.

So we have 445 ÷ 256 = 1 r 189

The quotient us what number goes with the place value of 256, which is 1.

Step 4) We now divide the remainder by the next (lower) power of 16.

So we have 189 ÷ 16 = 11 r. 13

The quotient us what number goes with the place value of 16, which is 11 (or B in hexadecimal).

Step 5) We now divide the remainder by the next (lower) power of 16.

So we have 13 ÷ 1 = 13

The quotient us what number goes with the place value of 1s, which is 13 (or D in hexadecimal).

Step 6) Put your place value parts together.

Our number 8637 = (2 x 4096) + (1 x 256) + (11 x 16) + (13 x 1).

So our hexadecimal answer is 21BD.

Or we could say (8637)₁₀ = (21BD)₁₆