0220. Why must we use the letters A, B, C, D, E, and F to represent the numbers 10, 11, 12, 13, 14, and 15 (respectively)?

By definition, a digit can be represented by a single symbol. In decimal, we have 10 symbols (0, 2, 3, 4, 5, 6, 7, 8, 9); there is NO single symbol to represent the number 10.

Because there are 16 digits in the hexidecimal system, we must create 6 additional symbols (A, B, C, D, E, and F). We can NOT, for example, use the symbols 11 to represent the number eleven. The number 11₁₆ is actually:

1 * 16¹ + 1 * 16⁰ = 16 + 1 = 17