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.
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You can easily convert decimal to binary in the scientific calculator - for example, the scientific calculator found in Windows. In this case, type the number in decimal, then click on "binary" to convert to binary.
The Binary system uses only the numbers 1 & 0. The decimal system has "dots" in them example of decimal: 1.25
No. The set of binary numbers includes fractions which are written in binary form. For example, binary(0.1) = decimal(0.5) which is not a natural number.
Decimal 11 = binary 1011
Binary 100 is 4 in decimal.