Don't Panic - Computer Arithmetic

Computer arithmetic is arithmetic with finite representations. An integer type covers a bounded set of whole numbers. A floating-point type covers a finite, unevenly spaced set of real-number approximations. That constraint explains wraparound, approximate decimal fractions, and why algebraically equivalent expressions can disagree on a machine.

Start with representation. A bit pattern needs a radix and an interpretation. Unsigned and two's-complement signed ranges differ for the same width. Overflow behavior is part of the language or ISA contract: wrap, trap, saturate, widen, or invalid. Never infer it from the bits alone.

Fixed-point arithmetic stores an integer with an implied scale. Floating-point stores a sign, significand, and exponent so one format can cover tiny and huge magnitudes with variable spacing. IEEE 754 defines common binary and decimal formats, rounding, exceptions, and special values such as infinities, NaNs, and subnormals. Each basic operation conceptually produces an exact result, then rounds to the destination format.

Rounding breaks familiar identities. Addition is not generally associative. Cancellation can magnify earlier error when you subtract nearly equal values. Choose bounded integers when you can prove range safety, decimal or scaled integers when decimal rules are the contract, and binary floating point when bounded approximation is acceptable. Specify types at interfaces and test boundaries deliberately.

Read the Intro for representation, rounding, and error vocabulary. Use the Cheatsheet when you need ranges, IEEE binary64 fields, and exception classes. Updates stays false because no single open official tracker covers the combined numeric contracts this course teaches.

Don't Panic - Computer Arithmetic

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