Floating Point — Binary Representation of Real Numbers
Understand how computers store real (decimal) numbers using floating point representation, including mantissa, exponent, normalisation, and precision trade-offs.
📚 Learning Steps
💡 Study Tips
- • Read through at your own pace
- • Try the interactive simulators hands-on
- • Study the pseudocode — it appears in exams
- • Quiz yourself before moving on
Step 1: Why Floating Point?
📖 TheoryComputers store everything in binary. While integers are straightforward, representing real numbers (numbers with fractional parts like 3.14) requires a different approach.
Fixed point representation uses a set number of bits for the integer part and a set number for the fractional part. This is simple but wastes bits — you can't represent very large or very small numbers efficiently.
Floating point solves this by letting the decimal (binary) point 'float' — similar to scientific notation in denary (e.g., 6.02 × 10²³).
🎯 Key Points
- •Fixed point: binary point is in a fixed position — limits range
- •Floating point: binary point can move — much wider range of values
- •Similar concept to scientific notation (e.g., 3.14 × 10²)
- •A floating point number has two parts: mantissa and exponent
- •Trade-off between range (exponent bits) and precision (mantissa bits)
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