What are the number systems? Define each and give it uses.?

in computer programming you have many number systems

binary = base 2 is the computers internal number system

its simple and has true or false or on or off only

but computer programming would be severely tedious if you had to do all the math in binary

there is also

octal and hexadecimal

octal is groups of 3 binary digits 2^3 = 8

so the number

101111010 in binary is

572 in octal

101 = 5

111 = 7

010 = 2

this is much easier to use and makes math a bit less tedius and inputting numbers too

then there is hexadecimal base 16

2^4 = 16 so its groups of 4 binary digits

the same number before becomes

the first 0's added to pad the number to 12 binary digits

000-101111010

0001 = 1

0111 = 7

1010 = A

so the number is 17A in hexadecimal

it is a much shorter number sometimes when you get into very long 32 bit and 64 bit words

so its advantage is ease of translation from hex to binary and from binary to hex and shortness so less mistakes when transcribing programs

both octal and hex were designed for humans to input the numbers into computers more efficiently with minimal conversions

there are many other versions of number systems Im not sure what the question is really asking because you also have

integer versus floating point

integer number systems are used for values where there is a definite integer value like 7 or 106 or 2045

or -756

all these have no fractional part and thus are considered integers..

then there is floating point number system its for representing a number that has a fractional part ..

1.5 is not an integer

so to represent 1.5 we have to devise a scheme for representing the integer part and the fraction part

the integer part is 1

the fraction part is 0.5

I'm not going into the different versions of floating point representation but that might be what your question was really asking

the simplest version of floating point would move the numbers all to the right of the decimal so that only a 0 on the left of course in binary

so the number 1.5 decimal would be

because 1 = 0001 binary

and 1/2 = 2^-1 = the first digit after the decimal

0001.1000

this is correct because if you times 1.5 by 2 you get the digits moving one place left and that make 11 or 3 decimal

and then move the decimal so that the first 1 is to the immediate right of the decimal

0.11000 * 2^1

so the mantissa would be 11000 the exponent would be 1

hope that helps

the other systems are decimal of course the one we are most familiar with ..