The result of an arithmetic operation is outside the range of allowable precision for the given number of bits is known as overflow in the context of unsigned numbers. 

A binary number with N bits can represent unsigned integers from 0 to 2^N-1.  

Using 4 bits it is possible to represent the decimal values 0 through 15 and 8 bits can represent the values 0 through 255.  

The range of values that can be represented by a given number of bits is extremely important when doing arithmetic operations on binary numbers.  

For example, consider the binary numbers are 4 bits in length, and we wish to add 1111₂ (15₁₀) to 1111₂. The sum 15 plus 15 is 30, but 30 cannot be represented using only 4 bits. This is an example of a condition known as overflow, which occurs in unsigned binary representation.