Definition 1: The number that gets multiplied when using an exponent.
Examples:
• in 82, 8 is the base, and the result is 8 × 8 = 64
• in 53, 5 is the base, and the result is 5 × 5 × 5 = 125
Definition 2: How many digits in a number system.
The decimal number system we use every day has 10 digits {0,1,2,3,4,5,6,7,8,9} and so it is Base 10.
A binary digit can only be 0 or 1, so is Base 2.
A hexadecimal digit can be {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}, so is Base 16.
