A Brief Explanation of Decimal, Binary and Hexadecimal Number
Systems
Base 10 and Positional Number Systems
We are all familiar with the base 10 number system that we use in our every day
lives. The base 10 number system is just one example of a positional number system. In a
positional number system a number is represented as a series of digits, where each digit
position is associated with a weight. For example, the number representing the year 2003
can be represented as follows:
2003 = 2 * 103 + 0 * 102 + 0 * 101 + 3 * 100
position 3 2 1 0
As you can see, each weight is the power of 10 to the number position starting at 0. The
* represents multiplication and any number raised to the power of zero = 1;
Binary and Hexadecimal Number Systems
Binary and Hexadecimal number systems are examples of positional number
systems with different bases. Binary number systems use a base of two while
hexadecimal uses a base of 16.
For example, the binary number 1010 is represented as follows:
1011 = 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20 = 1 * 8 + 0 * 4 + 1 * 2 + 1 * 1 = 11 (base 10)
For example, the hexadecimal number 123 is represented as follows:
123 = 1 * 162 + 2 * 161 + 3 * 160 * 0 = 1 * 256 + 32 + 3 = 291 (base 10)
In a hexadecimal system, it is necessary to count to 15. To represent the numbers 10 – 15,
the letters A – F are used respectively. To distinguish the different number systems,
suffixes or subscripts are often used.
Number system suffix example subscript example
decimal 0d 0d1023 10 102310
binary 0b 0b1101 2 11012
hexadecimal 0x 0x12F 16 12F16
The following table compares all three systems counting from 0 to 15.
