1. Number system Numbers 1) natural number:
zero and any number obtained by repeatedly adding one to it i.e ,653
2) negative number:
a value less then 1, with a – sign i.e -24,-1
3) integer:
a natural number, a negative number, zero i.e 248,0,-23

2. Number system
A set of values used to represent different quantities is called number system
i.e 1) number of student in class
2) number viewers watching TV.
There are four number system are as fellow:
Binary number system
Decimal number system
Octal number system
Hexadecimal number system

3. Decimal number system
The decimal number consist of 10 digits from 0 to 9.
These digits can be used to represent d/f any numeric value.
The base of decimal nuber system is 10.
It is most widely used number system.
The value represented by each digit depend on position and weight of digit.
The value of number is determined by multiplying the digits with the weight of their position and adding the result. This method is called expension method.

4. The right most digit of a number has the lowest weight
The right most digit of a number has the lowest weight. This digit is called least significant digit.
The left most digit of a number has the highest weight. This digit is called most significant digit.
The decimal number system is also called base ten or occasionally denary.
Example: 453
Position:
Weight:
Face value: 4 5 3
453 = 4*102+5*101+3*100
453 =
the actual number can be found by adding the values obtained by the digit.

5. Binary number system
Binary : it consist of 2 digits 0 and 1called bit. Byte: collection of 8 bits called 1 byte. Word: word consist of group of bits which are pressed around together during computition. * The word length of the computer system or processor is how many bits are grouped together.

6. 3) The base of binary number system is 2.
8 bit machine (i.e Nintendo Gameboy)
16 bit machine(sega genesis)
32 bit machine(sony playstation)
Binary number system
1) Digital computer are made up of electronic circui, which have exactly 2 ststes:ON and OFF.
2) Computer used numbering system which has exactly 2 symbols, representating on and off.
3) The base of binary number system is 2.
4) Each digit or bit in binary number system is 0 or 1.
5) Binary number system are built by concatenating a string of bits together.

7. As a general form:
dn*bn-1 + dn-1*bn-2+……………….+d1*b0
n: number of digits in number.
b: base
d: digit
i.E: 1011
When written,binary number are often subscripted,prefixed or suffixed in order to indicate their base.
The following notations are equivalent:
1011binary (explicit statement of fomat)
10111b (a suffix indicating binary format)
01101B (a suffix indicating binary format)
(a subscript indicating base-2(binary))

8. Base / Radix:
The total number of digits used in number system is called its base or radix.

9. Binary Numbers
Internally, information in digital systems is of binary form
groups of bits (i.e. binary numbers)
all the processing (arithmetic, logical, etc) are performed on binary numbers.
Example:
In decimal, (100101)2
Convention: write only the coefficients.
A = a1 a0 . a-1 a-2 a-3 where aj  {0, 1, …, 9}
How do you calculate the value of A?

10. Using the analogy, binary system {0,1} Example: 25.625
Decimal system
coefficients are from {0,1, …, 9}
and coefficients are multiplied by powers of 10
base-10 or radix-10 number system
Using the analogy, binary system {0,1}
base(radix)-2
Example:
= decimal expansion
= binary expansion =
base-r (n, m)
A = an-1 rn-1 +… + a1 r1 + a0 r0 + a-1 r-1 + a-2 r-2 + … +a-m r-m