In this system, numeric values are represented by using only two different symbols: typically 0 (zero) and 1 (one). The base 2 system is a positional numeric system with a radix of 2. Binary is the way computers hold information, by using only the two symbols: the 1's and the 0's.

Examples of binary numbers: 01, 10, 001, 010, 011, 100, 101, 110, 111, etc.

The decimal numeral system (some call it denary system) we're all familiar with is a base-ten system, meaning that it uses ten distinct digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Examples of numbers in the decimal system: 1, 2, 3, 10, 101, 304, 579, 2746, 54206, etc.

### Counting in binary system

After 0 and 1, next it comes 10. In fact, when counting, whenever we reach a number that is made up entirely only of 1's, an extra 1 digit is added to the left of that number (leftmost bit) and the rest of the bits are cleared (all 0's). This way, after the number 111 it follows the number 1000. This is very similar to what is happenning in the decimal system: when we reach a number that is made up entirely of only 9's, an extra digit set on 1 is added to the left of the number, while the rest of the bits are cleared (0's). After 999 next it comes 1000.

### Here are the first 32 (33) decimal system positive integer numbers (base 10) and their binary number representation equivalents (base 2):

0_{(10)} = 0_{(2)}; 1_{(10)} = 1_{(2)}; 2_{(10)} = 10_{(2)}; 3_{(10)} = 11_{(2)}; 4_{(10)} = 100_{(2)}; 5_{(10)} = 101_{(2)}; 6_{(10)} = 110_{(2)}; 7_{(10)} = 111_{(2)}; 8_{(10)} = 1000_{(2)}; 9_{(10)} = 1001_{(2)}; 10_{(10)} = 1010_{(2)}; 11_{(10)} = 1011_{(2)}; 12_{(10)} = 1100_{(2)}; 13_{(10)} = 1101_{(2)}; 14_{(10)} = 1110_{(2)}; 15_{(10)} = 1111_{(2)}; 16_{(10)} = 1 0000_{(2)}; 17_{(10)} = 1 0001_{(2)}; 18_{(10)} = 1 0010_{(2)}; 19_{(10)} = 1 0011_{(2)}; 20_{(10)} = 1 0100_{(2)}; 21_{(10)} = 1 0101_{(2)}; 22_{(10)} = 1 0110_{(2)}; 23_{(10)} = 1 0111_{(2)}; 24_{(10)} = 1 1000_{(2)}; 25_{(10)} = 1 1001_{(2)}; 26_{(10)} = 1 1010_{(2)}; 27_{(10)} = 1 1011_{(2)}; 28_{(10)} = 1 1100_{(2)}; 29_{(10)} = 1 1101_{(2)}; 30_{(10)} = 1 1110_{(2)}; 31_{(10)} = 1 1111_{(2)}; 32_{(10)} = 10 0000_{(2)}