Hexadecimal to Decimal Converter
Instantly convert hexadecimal decimal with our free converter. See conversion tables, formulas, and step-by-step explanations.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Decimal = Sum of (hex_digit x 16^position) | Hex = Repeated division by 16
Hexadecimal uses base 16 with digits 0-9 and A-F (representing 10-15). To convert hex to decimal, each digit is multiplied by 16 raised to its positional power and the results are summed. To convert decimal to hex, repeatedly divide by 16 and map remainders to hex digits.
Worked Examples
Example 1: CSS Color Code Conversion
Problem:Convert hex color #3CB371 (medium sea green) to its decimal RGB values.
Solution:Red: 3C hex = 3 x 16 + 12 = 60\nGreen: B3 hex = 11 x 16 + 3 = 179\nBlue: 71 hex = 7 x 16 + 1 = 113
Result:RGB(60, 179, 113)
Example 2: Memory Address Conversion
Problem:Convert the hexadecimal memory address 0x7FFF to decimal.
Solution:7 x 16^3 = 7 x 4096 = 28672\nF x 16^2 = 15 x 256 = 3840\nF x 16^1 = 15 x 16 = 240\nF x 16^0 = 15 x 1 = 15\nTotal = 28672 + 3840 + 240 + 15
Result:0x7FFF = 32,767 in decimal
Frequently Asked Questions
Why is hexadecimal used in computing?
Hexadecimal is widely used in computing because it provides a compact, human-readable representation of binary data. Each hex digit maps exactly to four binary digits (bits), making conversions straightforward. This is especially useful for representing memory addresses, color codes in web design (like #FF5733), MAC addresses, and byte values. A single byte (8 bits) can be represented by exactly two hex digits, ranging from 00 to FF.
What do the letters A through F mean in hexadecimal?
In hexadecimal notation, letters A through F represent the values 10 through 15 respectively. Since hexadecimal is base-16, it needs 16 unique symbols. The digits 0 through 9 cover the first ten values, and the letters A (10), B (11), C (12), D (13), E (14), and F (15) complete the set. Both uppercase and lowercase letters are valid and interchangeable in hex notation.
How do you convert decimal to hexadecimal?
To convert decimal to hexadecimal, repeatedly divide the decimal number by 16, recording each remainder. Convert any remainder of 10 or higher to its letter equivalent (10=A, 11=B, 12=C, 13=D, 14=E, 15=F). Continue dividing the quotient by 16 until it reaches zero, then read the hex digits from the last remainder to the first. For example, 255 divided by 16 is 15 remainder 15, then 15 divided by 16 is 0 remainder 15, giving FF in hex.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy