DAT 2343 Unsigned Binary Encoding Alan T Pinck

DAT 2343 Unsigned Binary Encoding © Alan T. Pinck / Algonquin College; 2003

The Most Common “Standard” Encoding System: Unsigned Binary is used to represent: n integer values n greater than or equal to zero n is used by almost every computer system as its basic numeric coding system n

Terminology bit n binary digit n (a binary circuit)

Positional Notation A 1 in any position represents a value which is one greater than the largest value that can be represented using on the digit positions to its right. Example: in the number 61543, the “ 1” represents one more than could be represented using the three positions to its right, that is one more than 999

Position Identification Example: An 8 -circuit collection (where each of the boxes represents one circuit which could be either 0/off or 1/on).

Bit Position Weights

Represented Value Based On Position Weights (using an 8 -bit/circuit example)

“Words” the number of circuits (wires) used to represent a basic encoded number (normally unsigned binary) is “hard-wired” in a computer when it is built. the number of circuits used by a specific computer to represent its basic numeric form is called the “word size” of that computer.

“Words” (continued) the actual collection of circuits used to represent a number in its basic encoded form (for some specific computer) is called a “word”. n note: in the terminology of computer architecture, a “word” relates to numbers, and not to what we normally mean by the term “word” in English.

Limitations Imposed By Word-Size A computer is limited in how large a number it can represent in its basic numeric coding system (usually unsigned binary). This limit is the value represented when all the circuits/bits of a “word” are turned “on”. Example: A computer using an 8 -bit word would have a maximum value which it could represent (in unsigned binary) of: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255

End of Lecture