Hexadecimal (base-16) uses digits 0–9 and letters A–F to represent values 0–15 in a single digit position. It is widely used in computing because each hex digit corresponds exactly to 4 binary bits (a nibble), making it a compact and readable shorthand for binary data. Memory addresses, color codes, and machine code are commonly expressed in hexadecimal. Converting between hex and binary is straightforward: replace each hex digit with its 4-bit binary equivalent.
Memorize the hex-to-binary mapping for 0–F. Practice converting byte values (8-bit = 2 hex digits) between all three bases. Read and interpret memory dumps and color codes expressed in hex.
Computers operate in binary — every piece of data is ultimately a sequence of 0s and 1s. But binary is painful for humans to read. The byte value `11010110` takes eight characters, and distinguishing it from `11010100` requires careful scanning. Decimal conversion helps with small values, but it obscures the bit-level structure that programmers often care about. Hexadecimal (base-16) solves this by providing a compact notation that preserves perfect alignment with binary: each hex digit maps to exactly 4 bits, so one byte is always exactly two hex digits, and conversion in either direction is instant.
The mapping is straightforward: 0 through 9 represent their usual values, and then A=10, B=11, C=12, D=13, E=14, F=15. To convert the binary byte `11010110` to hex, split it into two 4-bit groups: `1101` and `0110`. Looking up each group: `1101` = D and `0110` = 6, so the byte is `D6`. To go the other way, just expand each hex digit back to 4 bits. This mechanical, digit-by-digit conversion is what makes hex so useful — unlike decimal, there is no arithmetic involved, just a lookup table you quickly memorize.
Hexadecimal appears throughout computing. Memory addresses are written in hex because they are long binary values (32 or 64 bits) that would be unreadable in binary and misleading in decimal — the address `0x7FFF_FFFF` immediately tells an experienced programmer this is near the top of a 32-bit signed address space, while its decimal equivalent 2,147,483,647 does not convey that structure. Color codes in web design use hex: `#FF8800` means full red (FF = 255), about half green (88 = 136), and no blue (00 = 0). Machine code and assembly language listings display instruction bytes in hex. Debugging tools show memory dumps in hex. In each case, hex is preferred because it maintains a direct correspondence to the underlying bits while being roughly four times more compact than binary.
The prefix `0x` (used in C, Python, Java, and most programming languages) signals that a number is hexadecimal: `0x1A` is 26 in decimal, not eighteen or one-A. Some systems use other conventions — `$1A` in 6502 assembly, `1Ah` in Intel assembly, `#1A` in some contexts. Regardless of notation, the place-value system works identically to any other base: `0x1A` = 1×16¹ + 10×16⁰ = 16 + 10 = 26. As you move into memory organization and assembly language, hex will become your default way of reading and writing binary data — it is the lingua franca between human-readable and machine-readable representations.
This is a foundational topic with no prerequisites.
No prerequisites — this is a starting point.