Hex Calculator
What Is Hexadecimal and Why Developers Use It
Hexadecimal, often shortened to "hex," is a base-16 numbering system. Unlike the decimal (base-10) system we use daily, which has ten digits (0-9), hex uses sixteen symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and the letters A, B, C, D, E, F to represent values 10 through 15.
Developers love hex because it's a compact and human-readable way to represent binary (base-2) data. Computers work in binary, but long strings of 1s and 0s are difficult for people to read and manage. Each hexadecimal digit corresponds exactly to four binary digits (a "nibble"). For example:
- Hex
A= Binary1010 - Hex
F7= Binary1111 0111
This direct mapping makes it an essential tool for memory addressing, debugging, defining colors in web design (e.g., #FF5733), and working with low-level data structures.
How to Convert Hex to Decimal, Binary & Octal
Converting between number systems is a fundamental skill in computing. Our calculator automates this, but understanding the process is key.
- Hex to Decimal: To convert a hex number, multiply each digit by 16 raised to the power of its position (starting from zero on the right). For example,
2Bin hex is(2 * 16^1) + (11 * 16^0)=32 + 11=43in decimal. - Hex to Binary: This is the easiest conversion. Simply replace each hex digit with its 4-bit binary equivalent.
3Dbecomes0011(for 3) and1101(for D), so3Dis00111101in binary. - Hex to Octal: The simplest method is to first convert the hex number to binary, and then group the binary digits into sets of three from right to left, converting each group to its octal equivalent.
Hex Arithmetic & Bitwise Operations Explained
This calculator supports standard arithmetic and powerful bitwise operations critical for programming.
- Arithmetic (Add, Subtract, Multiply, Divide): These operations follow similar rules to decimal arithmetic, but you "carry over" or "borrow" in units of 16 instead of 10. For example,
8 + 9in hex is11(decimal 17), which is written as hex11(1 carry, 1 remainder). - Bitwise Operations (AND, OR, XOR, NOT): These operations work directly on the binary representation of the hex numbers. They are used for setting, clearing, or flipping specific bits in a number.
AND (&): A bit is 1 only if both corresponding bits are 1. Used for masking (keeping only certain bits).OR (|): A bit is 1 if either corresponding bit is 1. Used for setting bits.XOR (^): A bit is 1 if the corresponding bits are different. Used for toggling bits.NOT (~): Flips every bit (0 becomes 1, 1 becomes 0).
- Bit Shifts & Rotates: These operations move all bits in a number to the left or right, which is an efficient way to multiply or divide by powers of two. Rotates are similar, but bits that are shifted off one end wrap around to the other.
Working with Signed vs Unsigned Hex Values
A sequence of bits can be interpreted in two primary ways: as an unsigned number (always positive) or a signed number (can be positive or negative). The difference lies in how the most significant bit (MSB), the leftmost bit, is treated.
- Unsigned: All bits are used to represent the magnitude of the number. For an 8-bit number, the range is 0 to 255.
- Signed (Two's Complement): The MSB acts as a sign indicator. If it's
0, the number is positive. If it's1, the number is negative. The negative value is calculated using the two's complement method. For an 8-bit number, the range is -128 to 127. For example,0xFFis 255 unsigned, but it's -1 when interpreted as a signed 8-bit integer. Our calculator allows you to toggle between these interpretations for the decimal result.
Frequently Asked Questions
For more details, please see the structured data at the top of this page's source code, which provides answers to common questions about hexadecimal numbers and this calculator.
This calculator provides conversion and computation assistance for education and development. Always verify results for production-critical tasks.
