Computer arithmetic

1. Computer arithmetic Second try at third grade

2. What is stored and intended Bit patterns of several sizes, nothing more Almost all modern machines store and manipulate 1,2,4,8 byte quantities older ones had 12 ,40 ,36,60-bit words or decimal digit strings, or variable length BCD The bit patterns can represent: Numbers � fixed or floating point Text data � ascii, extended ascii or unicode Graphic data � pixels Bit patterns � I/O register contents � often packed Specialized data, sound or other signals, genomes

3. What operations are done These operations are usually in the ISA: Arithmetic operations on numbers � fixed or floating point The standard four functions (+, -, *, / %) Relational operations and comparison Conversions � float to fixed Logical operations on bit patterns � I/O register contents � often packed Bit operations � set, clear, flip Shifting and other bit field isolating methods Packing and unpacking are done with logic and shifting

4. Data for which few operations are defined Text data � ascii, extended ascii or unicode Graphic data � pixels, bitmaps, vector graphics Specialized data, sound or other signals, genomes

5. Number representation Several common varieties of multidigit number representation exist Most are directly descended from multidigit integer (positional notation) Several examples Sign and magnitude (people think this way) Two�s complement (or ten�s complement) Gray code (used to convert mechanical motion to glitchless binary)

6. Positional notation