What are number systemsexplain binary and decimal number systemwith example?

Answer 1

Take the number 1011

At first look you would say the value is one thousand and eleven and that is because we normaly think in terms of decimal numbers where the base is 10. In this system the digits are made up of 0,1,2,3,4,5,6,7,8,9. The number '10' itself (the base of this system) is formed by combining two of the primitive symbols (0 and 1). Base 10 means that the number 1011 has positional values of

(1 x 10^3) + (0 x 10 ^2) + (1 x 10^1) + (1 x 10^0), Note any number rasied to the power zero is 1. Thus our number is the same as adding

one thousand

zero hundreds

1 ten

1 one

But if I said the number is in binary the value is equivalent to decimal value '11'

This is because in the binary system of numbers the base is 2. In this system the digits are made up of 0,1. The number '2' itself (the base of this system) is formed by combining two of the primitive symbols (0 and 1). Base 2 means that the number 1011 has positional values of

(1 x 2^3) + (0 x 2 ^2) + (1 x 2^1) + (1 x 2^0), Note any number rasied to the power zero is 1. Thus our number is the same as adding

one eight

zero fours

1 two

1 one

As an exercise try defining the octal system representation of 1011 (Clue: The primitive digits are 0.1.2.3.4.5.6.7 and the number 8 itself (the base of this system is formed by combining two of the primitive symbols, 0 and 1). You should get a decimal quivalent of 521.

As an additional exercise try defining the hexadecimal system representation of 1011 (Clue: The primitive digits are 0.1.2.3.4.5.6.7,8,9,A,B,C,D,E,F and the number 16 itself (the base of this system is formed by combining two of the primitive symbols, 0 and 1). You should get a decimal quivalent of 4113.