What are (unsigned) number values
Important fact:
- Numeric values
are a
universal and
intrinsic
concept
|
Universal representation
of
numeric values:
This representation
in
cultural independent !!!
Some alternative
cultural-dependent
representations for unsigned numbers
Some alternative
cultural-dependent
representations for unsigned numbers
Some alternative
cultural-dependent
representations for unsigned numbers
Unsigned numeric value and its representation
Important fact:
- Numerical values are
intrinsic
- (Four is four in any culture)
- A numerical value
does not depend
on any
representation system used
- (Four can be represented differently in different culture)
|
We will examine
different representations
for numbers next.
2 types of representations systems for (unsigned) numbers
2 types of
representation systems for
(unsigned) integers:
- Non-positional
representation system
- Positional
representation system
|
Non-positional number representation
In non-positional representation:
- The value of a
digit (or "digit symbol") is
always the same
|
Example:
Roman Numbers
I = one
V = five
X = ten
L = fifty
C = hundred
|
Positional number representation
In positional representation:
- The value of a
digit (or "digit symbol")
depends
on its position
|
Example:
Decimal Numbers
in 12 the value of the digit 2 is two
in 24 the value of the digit 2 is twenty
|
Disadvantage
of non-positional number representation
Diadvantage:
- The non-positional representation
does not allow easy (simple)
arithmetic operations
|
Example: Roman
does not perform
addition like this:
Addition can be
performed easily in
a positional representation
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