What is the maximum number of shades of gray represented by a 4-bit binary number?

A 4-bit binary number consists of 4 bits, each of which can be either a 0 or a 1. Therefore, each bit doubles the number of possible combinations that can be formed. The total number of unique combinations that can be represented by a 4-bit binary number is calculated using the formula (2^n), where (n) is the number of bits.

In this case, since (n) is 4, the calculation is:

[

2^4 = 16

]

This means there are a total of 16 unique combinations that can represent different shades of gray. In digital imaging, each combination can be assigned a specific shade, ranging from black (0) to white (the maximum value represented by all bits being 1). Thus, the maximum number of shades of gray represented by a 4-bit binary number is 16.