Floating Points in Binary
Computer Science: OCR A Level, topic 4.1.14
Floating Point Representation
Floating point is a method of representing numbers in binary, which makes use of a binary point placed after the ‘most significant bit’ (MSB).
Floating point
- A floating point binary number is made up of two parts:
- The mantissa is the main number, containing a binary point after the MSB.
- The exponent determines where the binary point is positioned before the number is read.
- If the exponent is negative (i.e. it begins with a ‘1’), the binary point is moved left instead of right.
Converting to denary
- After the binary point has been moved, we can read the value of the mantissa.
- The denary value of the binary digit to the right of the binary point corresponds to:
- .
- Each subsequent binary digit corresponds to .. and so on.
Example
- The example below is a 12-bit floating point number, with an 8-bit mantissa and a 4-bit exponent:
- 0 . 1 0 1 1 0 0 0 0 0 1 1
- The exponent 0011 (which is equal to 3) identifies where the binary point should move in order to read the number.
Example cont.
- In this example, the binary point is moved 3 places to the right, which in turn subtracts 3 from the exponent:
- 0 1 0 1 . 1 0 0 0 0 0 0 0
- This represents the decimal number 5.5.