A base number system is a way to represent numbers using a specific set of digits. The most common system is the decimal system, which uses ten digits: 0 through 9. Other systems include the binary system, which uses two digits (0 and 1), and the hexadecimal system, which uses sixteen digits (0-9 and A-F). Each base indicates how many unique digits are available for counting. In a base number system, the value of a digit depends on its position. For example, in the decimal system, the number 345 means 3 hundreds, 4 tens, and 5 ones. Similarly, in the binary system, the number 101 represents 1 four, 0 twos, and 1 one, equating to the decimal value of 5.