Number Bases

Understanding Number Bases

  • A number base, or radix, is the number of unique digits, including zero, used to represent numbers in a positional numeral system.
  • Base-10 is the decimal system we use in everyday life, composed of ten digits from 0-9.
  • Base-2 or binary, used extensively in computing, only uses two digits, 0 and 1.
  • Base-16 or hexadecimal, is also commonly used in computing. It uses sixteen distinct symbols, usually 0-9 to represent zero to nine, and A-F to represent values ten to fifteen.

Conversion between Number Bases

  • Converting between number bases involves representing the same value in a different base.
  • Binary to decimal conversion involves summing up the products of each binary digit and 2 raised to the power of its position.
  • Decimal to binary conversion involves iteratively dividing by 2 and recording the remainders.
  • Conversion between binary and hexadecimal can be done easily as 16 is a power of 2 (2^4).

Importance of Different Number Bases in Computing

  • The binary system is fundamental to digital electronics and computing because it’s easy to represent binary digits, or bits, using two voltage levels.
  • Hexadecimal provides a more human-friendly way of representing binary sequences, as a single hexadecimal digit can represent a four-bit binary number (a nibble).
  • Understanding and being able to convert between number bases is critical when dealing with low-level programming, data manipulation, computer architecture, and networking, among other areas.