Question

when working with grayscale images, six or eight bits are common; However, if you have a four but system provide the calculation required to determine the number of shades of gray.

Answer 1

In a four-bit system, each bit has two possible values, resulting in 16 (2 to the power of 4) different shades of gray that can be represented.

Step-by-step explanation:

To determine the number of shades of gray that can be represented by a four-bit system, you need to understand that each bit can represent two values (0 or 1). In a four-bit system, we have four places where a bit could be either a 0 or a 1. Therefore, the calculation to find the number of different combinations (and thus the number of shades of gray) is 2 to the power of 4, which equals 16. This means in a four-bit grayscale image, you would be able to see 16 different shades of gray, from black to white. Here's a step-by-step explanation:

1. Understand that each bit can represent two values: 0 or 1.
2. Realize that in a four-bit system, you have four bits to represent shades of gray.
3. Use the formula 2ⁿ, where n is the number of bits, to calculate the number of shades.
4. Substitute 4 into the formula to get 2⁴ = 16.
5. Thus, a four-bit system can represent 16 different shades of gray.