Hex to Decimal Conversion (original) (raw)

Last Updated : 26 Sep, 2025

The hexadecimal number system, commonly known as base-16 or just hex, is a system of numbers that has 16 different symbols for representing various values.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Here: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

**Steps to convert Hexadecimal to Decimal

Using the base number 16, the hexadecimal to decimal conversion is performed.

**Step 1: From the table previously mentioned, write the number's hexadecimal equivalent in decimal form for each digit.

**Step 2: Beginning with the rightmost digit, multiply the digits in order from right to left with exponents of 16 i.e., 160, 161, 162, . . .

**Step 3: Following that, add each product. The decimal number is the sum of the results.

**Example: Convert 6CF (hex) to decimal.

**Solution:

6CF is the given hexadecimal number. In hexadecimal number system

• 6 = 6
• C = 12
• F = 15

Start at the unit's place of the number and multiply each digit by a power of 16 in order to convert this to a decimal number system.

6CF= (6 × 162) + (12× 161) + (15 × 160)
⇒ 6CF= (6 × 256 + 12 × 16 + 15 × 1)
⇒ 6CF= 1536 + 192 + 15
⇒ 6CF= 1743

**Thus, decimal value of 6CF is 1743.

**Hex to Decimal Table

You can use this table to convert hexadecimal digits to their decimal equivalents. For example, if you have the hexadecimal digit "A," you can look it up in the table to find that it is equivalent to the decimal number 10.

Hex to Decimal Formula

For the conversion to be complete, the multiple numbers must be added. The hexadecimal digit is expanded to multiply each digit by the power of 16, starting at 0 from the right and moving forward towards the right with the increase in power.

**Decimal Number = d n-1 **× 16 r-1 + d n-2 × 16 r-2 . . . + d 2 × 16 2 + d 1 × 16 1 + d 0 × 16 0

Where,

• **n is the number of digits, and
• **r is the placement of the digit (from the right side, starting from r = 0), and
• **d is the decimal value of the corresponding digit.

**Example: Convert 1A3 into decimal numbers.

**Solution:

Start from the rightmost digit i.e., 3. Its position is 0.
Decimal Value = 3 × 160 = 3 × 1 = 3

Move to the next digit i.e., A with a position of 1.

Since A represents 10 in decimal, the calculation becomes:

Decimal Value = 10 × 161 = 10 × 16 = 160

Finally, move to the leftmost digit i.e., 1 with a position of 2.

Decimal Value = 1 × 162 = 1 × 256 = 256

Thus, Decimal Value of 1A3 = 3 + 160 + 256 = 419

So, the hexadecimal number "1A3" is equivalent to the decimal number 419.

Try it yourself

Given below is a hex to decimal converter for easy calculation:

Hexadecimal to Other Number Systems

As hexadecimal is a number system, all numbers in decimal and other number systems can also be represented in the hexadecimal number system. The following table represents some numbers in hexadecimal, decimal, octal, and binary as well.

**Related Articles

• Binary to Decimal Converter
• Binary to Hexadecimal Converter

**Solved Problems on Hex to Decimal

**Problem 1: Convert 31.D216.

**Solution

As we know,

Digit	3	1	D	2
Place value	161	160	16-1	16-2

31.D216 = (3×161) + (1×160) + (D×16-1) + (2×16-2)

⇒ 31.D216 = 48 + 1 + 13×16-1 + 2×16-2

⇒ 31.D216 = 48 + 1 + 0.8125 + 0.0078125

⇒ 31.D216 = 49.8203125

**Problem 2: Convert (4C7) to a decimal number.

**Solution:

In Hexadecimal Number System,

4= 4, C = 12, and 7 = 7

Hence, (4C7)16 = (4× 16²) + (12 × 16¹) + (7 × 16⁰)
⇒ (4C7)16 = (4 × 256) + (12 × 16) + (7 × 1)
⇒ (4C7)16 = 1024 + 192 + 7
⇒ (4C7)16 = 1223

Therefore, (4C7)16 = (1223)10

Problem 3: Convert (16F) into its equivalent Decimal number.

**Solution:

We have a hexadecimal number 16F that we want to convert into a decimal number.

We know that 1 = 1, 6 = 6 and F = 15.

Therefore (16F)16 = (1 × 162) + (6 × 161) + (15 × 160)

⇒ (16F)16 = (1 × 256) + (6 × 16) + (15 × 1)
⇒ (16F)16 = 256 + 96 + 15
⇒ (16F)16 = (367)10

Hence, (16F)16 to decimal is 367.

**Problem 4: Convert 5BC (hex) to decimal.

**Solution:

We know that 5 = 5, B = 11 and C = 12.

Therefore (5BC)16 = (5 × 162) + (11 × 161) + (12 × 160)

⇒ (5BC)16 = (5 × 256) + (11 × 16) + (12 × 1)
⇒ (5BC)16 = 1280 + 176 + 12
⇒ (5BC)16 = (1468)10

Hence, (5BC)16 is 1468 in decimal number system.

**Problem 5: Convert (5EC)16 to decimal.

**Solution:

As we know,

In hexadecimal system, E = 14,

∴ (5EC)16 = (5 × 16²) + (14 × 16¹) + (12 × 16⁰) = 1516

Hence, (5EC)16 = (1516)10

**Problem 6: Convert 4CD from Hexadecimal to Decimal.

**Solution:

We know that 4 = 4, C = 12, and D = 13 in hexadecimal (hex).

Therefore, to convert the hexadecimal number 4CD to decimal, we can use the positional notation method:

(4CD)₁₆ = (4 × 16²) + (12 × 16¹) + (13 × 16⁰)
⇒ (4CD)₁₆ = (4 × 256) + (12 × 16) + (13 × 1)
⇒ (4CD)₁₆ = 1024 + 192 + 13
⇒ (4CD)₁₆ = (1229)₁₀

Hence, 4CD (hex) to decimal is 1229.

**Problem 7: Convert 1AB from Hexadecimal to Decimal.

**Solution:

We know that 1 = 1, A = 10, and B = 11 in hexadecimal (hex).

Therefore, to convert the hexadecimal number 1AB to decimal, we can use the positional notation method:

(1AB)₁₆ = (1 × 16²) + (10 × 16¹) + (11 × 16⁰)
⇒ (1AB)₁₆ = (1 × 256) + (10 × 16) + (11 × 1)|
⇒ (1AB)₁₆ = 256 + 160 + 11
⇒ (1AB)₁₆ = (427)₁₀

Hence, 1AB (hex) to decimal is 427.

**Problem 8: Convert 5BC (hex) to decimal.

**Solution:

We know that 5 = 5, B = 11 and C = 12.

Therefore, (5BC)16 = (5 × 162) + (11 × 161) + (12 × 160)
⇒ (5BC)16 = (5 × 256) + (11 × 16) + (12 × 1)
⇒ (5BC)16 = 1280+176+12
⇒ (5BC)16 = (1468)10

Hence, 5BC (hex) to decimal is 1468.

Problem 9: Convert 1D9 (hexadecimal) to decimal.

**Solution:

In the Hexadecimal system,

1 = 1, D = 13, and 9 = 9

(1D9)16= (1 × 162 + 13 × 161 + 9 × 160 )
⇒ (1D9)16 = 1 × 256 + 13 × 16 + 9 × 1
⇒ (1D9)16 = (473)10

Practice Problems on Hex to Decimal

**Problem 1: Convert the hexadecimal number "1A" to decimal.

**Problem 2: Change hexadecimal to decimal for the value "2F."

**Problem 3: Converting hexadecimal to decimal, what is the decimal representation of "7B"?

**Problem 4: Use a hexadecimal to decimal converter to find the decimal equivalent of "3D8."

**Problem 5: How to change hex to decimal for the hexadecimal number "FFFF"?

**Problem 6: How do you convert hex to decimal for the value "4A5"?

**Problem 7: From hex to decimal, calculate the decimal value of "B2E" in hexadecimal.

**Problem 8: Hex to decimal: Find the decimal value of "5C."

**Problem 9: What is the process of converting "1E4" from hexadecimal to decimal?

**Problem 10: Convert the value "AA" from hexadecimal to decimal and then to binary.