Oxford, Cambridge and RSA (OCR) GCSE Computer Science Paper 2 Practice

The total number of colors that can be represented based on the number of bits per pixel is expressed by the formula \( 2^n \), where \( n \) is the number of bits. Each bit can have two possible values: 0 or 1. Therefore, for each additional bit added, the number of possible combinations—and consequently, the number of different colors that can be represented—doubles.

For example, if there is 1 bit per pixel, there are \( 2^1 = 2 \) colors. If there are 2 bits per pixel, there are \( 2^2 = 4 \) colors. Generally, with \( n \) bits, the total combinations are \( 2^n \), allowing for a rapid increase in color variability with just a few additional bits.

The other answers do not accurately represent the relationship between the number of bits and the number of colors. Options like \( n^2 \) suggest that colors could be represented in a quadratic manner, which does not capture the binary nature of bits. \( n! \) represents the factorial of \( n \), which relates to permutations, not color representations. Lastly, \( 3*n \) implies a linear