Question

What is hierarchy for numbers, and what are 3 different number bases used when thinking about computers. g

Answer 1

Hierarchy of numbers is called to the classification given to numbers. More details given below.

Number Base is the amount on distinct symbols used for each digit. Usual number bases in computers are: Binary, Decimal and Hexadecimal.

Explanation:

Hierarchy of numbers

The numbers are classified in several nested groups: Complex, Imaginary, Real, Irrational, Rational, Fraction, Integer, Natural, Zero and Negative. There is a diagram attached that illustrates the order, hierarchy and examples of each group.

Number Base

Binary base uses 2 different numbers for each digit: 0 and 1.

Decimal base uses 10 different numbers for each digit: 0,1,2...9.

Hexadecimal base uses 16 different numbers for each digit: 0,1,2...9,A,B,C,D,E,F.

For each base, the digit position has a different value that can be generalized as:

`base^(position-1)`

so, the number 123 in decimal (base 10) can also be written as:

`1*{10^(2) }+2*10^(1) +3*10^(0)`

or 4A9 in hexadecimal (base 16) is:

`4*16^2+A*16^1+9*16^0`

I have attached a table with some example numbers for each of these number bases.