Base number
Can the numbers 110101 and 53 be equal? Of course not, if both are interpreted as numbers in the normal decimal system. However, the situation is different if the figures are interpreted to be represented in different numeral systems.
Numeral systems are named according to their base number. The base number also determines the types of numbers that can be formed in the numeral system.
Numeral systems are named according to their base number. The base number also determines the types of numbers that can be formed in the numeral system.
The base number tells which numbers the numeral system contains
If the base number of a numeral system is the natural number [[$ <em>n $]], the following numbers can be part of the numeral system: [[$ 0,1, 2, 3, ..., n-1 $]]
The most common numeral system is the decimal system. The base number of the decimal system is 10, and the numbers 0 ... 9 appear in it. In the decimal system, each number can be written using a scientific expression. In calculators, the decimal system is denoted by the abbreviation DEC.
Example 1
The number 374 can be written in the form
[[$ 3 \cdot 100 + 7 \cdot 10 + 4 \cdot 1 \qquad $]] or [[$ \qquad 3 \cdot 10^2 + 7 \cdot 10^1 + 4 \cdot 10^0 $]]-