What is the minimum number of memory bits necessary to display how many shades of gray?

To determine the minimum number of memory bits required to display shades of gray, it's essential to understand how bits contribute to representing different values. Each bit can represent two states: 0 or 1. Therefore, the number of possible values or levels of gray that can be represented by a given number of bits is calculated using the formula: (2^n), where (n) is the number of bits.

For example:

• With 1 bit, you can represent (2^1 = 2) shades (black and white).

• With 2 bits, you can represent (2^2 = 4) shades.
• With 3 bits, you can represent (2^3 = 8) shades.
• With 4 bits, you can represent (2^4 = 16) shades.
• With 5 bits, you can represent (2^5 = 32) shades.
• With 6 bits, you can represent (2^6 = 64) shades.
• With 7 bits, you can represent (2^7 = 128) shades.

Thus, to display a minimum of 128 shades of gray, you need 7 memory bits