Find the number of bits required to store a 256 X 256 image with 32 gray levels

To determine the number of bits required to store a 256 x 256 image with 32 gray levels, follow these steps:

1. Understanding Gray Levels:

   • A 32 gray level image means each pixel can have one of 32 shades of gray.
   • This requires ⌈log?2(32)⌉\lceil \log_2(32) \rceil⌈log2?(32)⌉ bits per pixel to represent all possible gray levels.

2. Calculate Bits per Pixel:

   log?2(32)=5\log_2(32) = 5log2?(32)=5
   • Therefore, each pixel requires ⌈5⌉=5\lceil 5 \rceil = 5⌈5⌉=5 bits to represent 32 gray levels.

3. Calculate Total Number of Pixels:

   • A 256 x 256 image has:
   256×256=65,536 pixels256 \times 256 = 65,536 \text{ pixels}256×256=65,536 pixels

4. Calculate Total Storage Requirement:

   • Multiply the number of pixels by the number of bits per pixel:
   65,536×5=327,680 bits65,536 \times 5 = 327,680 \text{ bits}65,536×5=327,680 bits

5. Convert to Bytes (Optional):

   • To convert bits to bytes, divide by 8 (since 8 bits = 1 byte):
   327,6808=40,960 bytes\frac{327,680}{8} = 40,960 \text{ bytes}8327,680?=40,960 bytes

Therefore, to store a 256 x 256 image with 32 gray levels, you would need 327,680 bits or 40,960 bytes of storage space. This calculation assumes each pixel is represented with 5 bits to accommodate 32 different gray levels per pixel.