How this tool fits your workflow
How positional number systems work
Every positional number system uses a base (radix). Decimal (base 10) uses digits 0-9. Binary (base 2) uses 0-1. Octal (base 8) uses 0-7. Hexadecimal (base 16) uses 0-9 plus A-F for values 10-15. The position of each digit represents a power of the base: rightmost is base^0, next is base^1, and so on.
Example: decimal 255 = 2 times 10^2 + 5 times 10^1 + 5 times 10^0. Binary 11111111 = sum of 2^7 through 2^0 = 255. Hex FF = 15 times 16 + 15 = 255. All three represent the same value.
Practical uses in programming
Hex is everywhere in low-level programming: memory addresses (0x7FFE4C2B), byte masks (0xFF), CSS color values (#3B82F6 = R:59, G:130, B:246), and bitwise operations. Binary is used when individual bits matter: permission flags, protocol headers, and bitwise AND/OR operations.
Octal still appears in Unix permissions. chmod 755 sets owner=rwx (7=111 in binary), group=r-x (5=101), others=r-x (5=101). Understanding the octal-to-binary relationship makes permission strings intuitive.
Frequently asked questions
- How do I convert decimal to binary?
- Repeatedly divide by 2 and record remainders bottom to top. For 25: 25/2=12R1, 12/2=6R0, 6/2=3R0, 3/2=1R1, 1/2=0R1. Read remainders bottom to top: 11001.
- Why do programmers use hexadecimal?
- Each hex digit represents exactly 4 binary bits, making hex a compact human-readable representation of binary data. Two hex digits equal one byte. Memory addresses, color codes, and binary file data are naturally expressed in hex.
- What is octal used for?
- Octal mainly appears in Unix file permissions (chmod 755 means rwxr-xr-x). Each octal digit represents 3 binary bits.
- Can this converter handle negative numbers?
- Yes. Negative numbers show with a minus sign in all bases. For two's complement (how computers store negatives), the representation for -N in n bits is (2^n) - N.