Give you example of numeration system?

Answer 1

Examples of a numeration system are:

Base 10 or decimal. This system (which is the system that everyone is familiar with) has ten digits 0, 1, 2, 3, 4, 5 6 7 8 and 9. The least significant column has a weighting of 1, the next column to the left a has a weighting of 10 and each successive column to the left has a weighting 10 times that on the column on it's right.

Base 2 or binary. This system has only 2 digits 0 and 1. The least significant column has a weighting of1, the next column to the left has a weighting of 2 and each successive column to the left has a weighting 2 times that on the column on it's right.

EXAMPLES 1 10 11 100 101 110 111 are the equivalent of the decimal numbers 1 2 3 4 5 6 7.

Base 8 or octal. This system has 8 digits 0 1 2 3 4 5 6 and 7. The least significant column has a weighting of1, the next column to the left has a weighting of 8 and each successive column to the left has a weighting 8 times that on the column on it's right.

EXAMPLES 5 6 7 10 11 12 13 14 are the equivalent of the decimal numbers 5 6 7 8 9 10 11 12 or in binary 101 110 111 001000 001001 001010 001011 001100. 3 binary digits are used to represent each octal digit so octal 12 001 for the 1 and 010 for the 2 shown as 001010. It is normal to group the binary digits into 3's like this 001 010

Base 16 or hexadecimal. This system has 16 digits 0 1 2 3 4 5 6 7 8 9 A B C D E and F. The least significant column has a weighting of1, the next column to the left has a weighting of 8 and each successive column to the left has a weighting 8 times that on the column on it's right.

EXAMPLES 8 9 A B C D E F 10 11 12 are equivelant to the decimal numbers 8 9 10 11 12 13 14 15 16 17 18 or to the binary numbers 1000 1001 1010 1011 1100 1101 1110 1111 00010000 00010001 00010010

note that 15 decimal = F hexadecimal = 1111 binary. Each hexadecimal digit is represented by four binary digits; so 12 hexadecimal has four binary digits to represent the 1 and another four digits to represent the 2 i.e. 0001 and 0010. Shown as 00010010.

It is normal to group the binary digits in this case into 4's like this 0001 0010