NUMBER SYSTEMS

                           NUMBER SYSTEM :-

•   Number system is  defined as the magnitude of any quantity.
•  We have four Number system techniques.

1. Binary Number system
2. Octal Number system
3. Decimal Number system 
4. Hexa decimal Number system

• Base / Radix is Nothing but the value. Generally it's represents the number of digits / Symbols are used in the number system.
• Any number system starts  { 0} and ends with { r-1} .
• "r "   represents base / radix of a number system.

BINARY NUMBER SYSTEM :-

• Generally  the  base of  Binary number system is 2.

                          i.e   r=2

• So In Binary number system we are used only two digits.  

                         i.e   { 0,  1 }

OCTAL NUMBER SYSTEM :-

• Generally  the  base of  Octal number system is 8.

                          i.e   r=8

• So In Binary number system we are used only eight  digits.  

                         i.e   { 0,  1, 2, 3, 4, 5, 6, 7  }

DECIMAL NUMBER SYSTEM :-

• Generally  the  base of  Decimal number system is 10.

                          i.e   r=10

• So In Binary number system we are used only ten digits.  

                         i.e   { 0,  1, 2, 3, 4, 5, 6, 7, 8, 9  }

HEXA DECIMAL NUMBER SYSTEM :-

• Generally  the  base of  Hexa  Decimal number system is 16.

                          i.e   r=16

• So In Binary number system we are used only sixteen  digits. After 9 we are used Alphabets {A, B, C, D, E, F / a, b, c, d, e, f } 

                         i.e   { 0,  1, 2, 3, 4, 5, 6, 7, 8, 9,  A, B, C, D, E, F }

            NUMBER SYSTEM CONVERSIONS

DECIMAL TO ANY OTHER NUMBER SYSTEM

       It having the algorithm for this one we can follow below steps

1. Divide  the decimal number to be converted by the value of base / radix
2. Get the remainder from step-1 and kept right side and quotient kept down of the decimal value
3. Divide the quotient of the previous divided by new base 
4. Repeat the step- 3 when the quotient is less than the new base number
5. finally all the remainder come together form a number. It is a required number system of a number.

DECIMAL TO BINARY NUMBER SYSTEM : -

DECIMAL TO OCTAL NUMBER SYSTEM :-

DECIMAL TO HEXA DECIMAL NUMBER SYSTEM : -