Convert “0x1F” to decimal. Only input the decimal number, nothing else.
The correct answer and explanation is:
31
The hexadecimal number system, often referred to as base-16, is widely used in computing and digital electronics. It uses sixteen distinct symbols: 0 to 9 represent values zero to nine, and the letters A to F represent values ten to fifteen. When converting from hexadecimal to decimal (which is base-10), each digit in the hexadecimal number is multiplied by 16 raised to the power of its position, starting from zero on the right.
The hexadecimal number “0x1F” represents the number 1F in base-16. To convert this to decimal, start by breaking it down into individual digits:
- The digit “F” is equivalent to 15 in decimal.
- The digit “1” is equivalent to 1 in decimal.
Then apply the base conversion formula:
(1 × 16¹) + (15 × 16⁰)
= (1 × 16) + (15 × 1)
= 16 + 15
= 31
So, the decimal equivalent of 0x1F is 31.
This type of conversion is essential in computer science because computers use binary and hexadecimal numbering systems internally, and humans often need to interpret or input data using more readable decimal notation. Understanding hexadecimal is especially useful when dealing with memory addresses, color codes in web design, machine code, and low-level programming. Hexadecimal values are more compact than binary and are easier to read and write for humans, while still being closely related to binary. For example, one hexadecimal digit represents four binary digits, or bits, making conversions between binary and hexadecimal straightforward. This close relationship is what makes hexadecimal a favored choice for representing binary values in a more concise format.