Floating Point & Character Representation (SQA National 5 Computing Science): Revision Note

Floating point

What is floating point?

• Computers use floating point to store real numbers, numbers that have a fractional part

• Floating point representation is similar to scientific notation, but it uses base 2 (binary) instead of base 10 (denary)

• A floating point number is made up of two parts:

  • The mantissa

  • The exponent

Mantissa

• The part of the number that holds the sequence of significant digits that make up the number

• Controls the precision of the number

• Does not change the scale of the number

Exponent

• The part that shows how far the binary point moves

• Controls the size or scale of the number

• A larger exponent moves the point to the right (making a larger number)

• A smaller exponent moves the point to the left (making a smaller number)

Example

• In scientific notation

  • 0.8916 × 10³

• Mantissa = 8916

• Exponent = 3

• The same idea applies in binary, but it uses powers of 2 instead of powers of 10

Extended ASCII

What is extended ASCII?

• Extended ASCII is a character set used to represent text on a computer system

• It uses 8 bits for each character, giving 256 unique codes (2⁸ = 256)

• Each character, letters, numbers or symbols, is given a unique binary code

• This means that text can be stored and processed consistently on different computer systems

How extended ASCII is used

• Extended ASCII is used to represent:

  • Upper and lower case letters

  • Numbers 0–9

  • Punctuation marks and special characters (for example !, @, #, £)

  • Additional symbols such as mathematical signs or accented letters

Calculating storage using extended ASCII

• Each character requires 8 bits (1 byte) of storage

• Formula:

  • Bits required = number of characters × 8

• Examples:

  • “SERVER” has 6 characters → 6 × 8 = 48 bits

  • “GRK_0183_J” has 10 characters → 10 × 8 = 80 bits

  • “Par Tee” has 7 characters (including the space) → 7 × 8 = 56 bits

• Sometimes you may be asked the reverse calculation:

• Formula:

  • Characters stored = total bits ÷ 8

• For example, 80 bits ÷ 8 = 10 characters