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Computer Representation of Numbers and Computer Arithmetic

Subsections

Binary numbers
Memory
- Characters in Memory
- The Memory Model
Reprentation of Signed Integers
- Integers in Memory
- Note.
Floating-Point Numbers
The IEEE standard
- Floating Point Types
- Detailed IEEE representation
- Number range
- Precision
The Set of FP Numbers
Rounding - up or down
Chopping
Rounding to nearest.
Arithmetic Operations
IEEE Arithmetic
The Guard Digit
Special Arithmetic Operations
- Signed zeros
- Operations with
- Operations with NaN
- Comparisons
Arithmetic Exceptions
- Division by 0
- Overflow
- Underflow
- Inexact
- Summary
Flags and Exception Trapping
Systems Aspects, from D. Goldberg, p. 193
- Instruction Sets
- Ambiguity
- Programming Language Features
- Optimizers
- Exception Handling
Long Summations
Tipical pitfalls with floating point programs
- Binary versus decimal
- Floating point comparisons
- Funny conversions
- Memory versus register operands
- Cancellation (``Loss-of Significance'') Errors
- Insignificant Digits
- Order of Operations Matters
Integer Multiplication
Homework

Adrian Sandu 2001-08-26