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616 Appendix

1. Dimensions

1.1 Definition of dimension, repeated from GC 12.

dimension : = (base-unit: unit)½ [dimension-expression]

1.2 Basic dimensions

time / [t] : = dimension(base-unit: second)

length / [l] : = dimension(base-unit: meter)

cost / [\$] : = dimension(base-unit: dollar)

weight : = dimension(base-unit: kilogram)

power : dimension(base-unit: watt)

temperature : = dimension(base-unit: degree-centigrade)

voltage : = dimension(base-unit: volt)

current : = dimension(base-unit: ampere)

component / [c] : = dimension

operation / [o] : = dimension

information / [i] : = dimension(base-unit: bit)

state : = dimension(base-unit: state)

2. General units

2.1 Definition of unit, repeated from CC 12.

unit : = (dimension; conversion-list)½ unit-name : = multiplier unit½ simple-name

conversion : = number-name unit ½ number-name / unit½ arithmetic-expression (unit)

2.2 We give the basic units, but no variations with multipliers.

second / sec / s : = unit(dimension: time)

minute / min : = unit(dimension: time; conversion: 60 s)

meter / m : = unit(dimension: length)

foot / ft : = unit(dimension: length; conversion: 3.28 / meter, 12 in)

inch / in : = unit(dimension: length; conversion: 39.37 / meter, 12 / ft)

dollar / \$ : = unit(dimension: cost)

operation / o : = unit(dimension: operation)

watt / w : = unit(dimension: power)

volt / v : = unit(dimension: voltage)

ampere / amp / a : = unit(dimension: current)

kilogram / kg : = unit(dimension: weight; conversion: 2.2 / lb)

pound / lb : = unit(dimension: weight; conversion: 2.2 kg)

3. Information units

3.1 Units

state : = unit(dimension: state; conversion: 2x bits)

binary-digit / bit / b : = unit(dimension: [i]; conversion: log2(x) states)

octal-digit / od : = unit(dimension: [i]; conversion: 3 bits)

decimal-digit / digit / d / dit rare: unit(dimension: [i]; conversion:
log2(10) bits, 1og10(x) states)

hexa-decimal-digit / hex : = unit(dimension: [i], conversion: 4 bits)

character / char / ch : = unit(dimension: [i]; conversion: 4 ~ 8 bits)

byte / by : = unit(dimension: [i]; conversion: 8 bits)

COMMENT The byte is almost standardized at 8 bits; occasional use otherwise, although not in this book.

3.2 I-units

i-unit : = base-unit ½ length X i-unit½ i-unit-name ½ (base-unit; length- list; content: product(length-list) base-unit; level:number(length-list))
i-unit-name : = i-unit-prefix i-unit-name ½ simple-name
i-unit-prefix : = + integer½ multiple/m½ quadruple/q½ triple/t½ double/d ½ *single/s ½ half/h ½ fractional/fr

base-unit : = unit(dimension: [i])
length : = + integer

The i-unit is a hierarchically organized information structure, in which each level consists of a number of subunits, all identically organized. The number of subunits in a level is called its length. Units eventually occur that cannot be decomposed further. These are called base-units and are some unit of information-e.g., the bit or the character. Thus, if the lengths are L1, L2, . . . , Ln and the base unit is the bit, then the total amount of information (the content of the i-unit) is L1 x L2 x . . . x Ln bits and the number of levels is n. The i-unit may be likened to an n-dimensional rectangular volume of information (except that the "dimensions"¾ the lengths¾ occur in a fixed order).

COMMENT Almost all information in computer systems is organized in terms of i-units¾ e.g., a memory consists of a number of words, each of a number of characters, each of a number of bits. More exotic data structures are invariably encoded into i-units and are not reflected in the hardware.

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