Key facts

  • 1679: Gottfried Wilhelm Leibniz described binary arithmetic using 0 and 1, giving modern computing its most important number-base idea.
  • 1937: Claude Shannon showed that Boolean algebra could describe switching circuits, linking binary logic with digital hardware design.
  • 1947: John W. Tukey coined the word "bit" as a short form of binary digit, now the basic unit of digital information.
  • 1963: the American Standards Association published ASCII as ASA X3.4-1963, standardising 7-bit character coding for computers and communication.
  • 1964: IBM announced System/360, a major computer family that helped make the 8-bit byte a common practical storage unit.

Key Points at a Glance

  1. 1

    1679: Gottfried Wilhelm Leibniz described binary arithmetic using 0 and 1, giving modern computing its most important number-base idea.

  2. 2

    1937: Claude Shannon showed that Boolean algebra could describe switching circuits, linking binary logic with digital hardware design.

  3. 3

    1947: John W. Tukey coined the word "bit" as a short form of binary digit, now the basic unit of digital information.

  4. 4

    1963: the American Standards Association published ASCII as ASA X3.4-1963, standardising 7-bit character coding for computers and communication.

  5. 5

    1964: IBM announced System/360, a major computer family that helped make the 8-bit byte a common practical storage unit.

  6. 6

    1991: Unicode 1.0 was released, beginning a universal character-coding standard intended to cover the scripts used across the world.

  7. 7

    1993: ISO/IEC 10646-1 was first published, aligning international character-set work with the Unicode model for wider software interoperability.

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Positional notation and bases

Number systems used in computers are positional systems. In a positional system, the value of a digit depends on the digit itself and its place. Decimal 572 means 5 hundreds, 7 tens and 2 ones because decimal uses base 10. The same idea works in binary, octal and hexadecimal; only the base changes. For any base b, the places to the left of the point are powers of b: b^0, b^1, b^2 and so on. Places to the right are negative powers such as b^-1 and b^-2. This is why 101 in binary is not one hundred and one; it is 1 x 2^2 plus 0 x 2^1 plus 1 x 2^0, so its decimal value is 5.

A digit in a base must be smaller than the base. Binary permits only 0 and 1. Octal permits 0 to 7. Decimal permits 0 to 9. Hexadecimal permits 0 to 9 and A to F, where A means 10 and F means 15. In an MCQ, an invalid digit is often the fastest clue: 128 cannot be an octal number because 8 is not an octal digit.

Remember this: base tells both the allowed digits and the place values.

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