Binary basics
Binary numbers use base 2 with the digits 0 and 1, mirroring the on/off states of digital electronics.
- Each bit represents an increasing power of two from right to left.
- Eight bits form a byte that stores values from 0 to 255.
Decimal in daily life
Decimal is the base-10 system most people use because it aligns with counting on ten fingers.
- Place values grow by powers of ten (ones, tens, hundreds, ...).
- Financial records and measurements almost always use decimal.
Hexadecimal shortcuts
Hexadecimal uses base 16 with digits 0-9 and letters A-F, making it compact for representing large binary values.
- One hex digit maps to exactly four binary bits.
- Hex is widely used to display memory addresses and color codes.
Conversion tips
Group digits and use positional values to convert between bases without mistakes.
- Binary ↔ Decimal: sum powers of two or repeatedly divide by two.
- Decimal ↔ Hex: divide by sixteen or regroup binary bits into nibbles.
- Binary ↔ Hex: translate every four bits to a single hex character.
Where each base is used
Different bases shine in different contexts.
- Binary powers modern computing hardware and low-level protocols.
- Decimal dominates human communication, finance, and documentation.
- Hexadecimal bridges human readability with binary precision in development tools.