Thank you for the help. Thank you for the help.

Question

Thank you. Thank you. Thank you.

Answer 1

Gwen,

When a base is not specified explicitly (using a subscript), then the assumed base for arithmetic is base 10. This is because humans have 10 fingers (normally), and fingers were one of the original calculating/counting tools (this is why fingers are called digits). Thus, base 10 is called the common base, and there is no need to explicitly specify it with a subscript (but you can if you want to). Below are the results of 2 + 2 in bases from 2 up to 10. Notice that as long as the the base is greater than the quantity of the result (4), then the the quantity can be represented by the digit "4" in that base. This is because a particular base (base N) only has digits that range from 0 up to N-1.

10₂ + 10₂ = 100₂

2₃ + 2₃ = 11₃

2₄ + 2₄ = 10₄

2₅ + 2₅ = 4₅

2₆ + 2₆ = 4₆

2₇ + 2₇ = 4₇

2₈ + 2₈ = 4₈

2₉ + 2₉ = 4₉

2₁₀ + 2₁₀ = 4₁₀