# Maximum Number of images

How many images can be produced by all permutations of 24-bit 640x480 JPEG? Is this is the maximum number of images on 24 bit 640x480 frame and we can not have more images?

• Is this homework? – frabjous Jan 18 '11 at 4:17
• No it is not home work. I had a discussion with one of my friend.The concern is that is the number of images limited on a particular scale. I think no. – Any Jan 18 '11 at 4:25

## 1 Answer

(2^24)^(640x480)

2 choices per bit

24 bits

640 times 480 pixels

^ is exponent

~~ edit to reply to comments~~

Yes, this is the maximum number of images.

Yes, compression would decrease this number.

More basic example, to clarify:

Let's calculate how many images can be 1x2 using 2 bit color.

In 2 bit color, each pixel must be one of 4 colors. In my imaginary world, here, the choices are Black, White, Green and Yellow: BWGY

So, for pixel 1,1, there are 4 choices. And for pixel 1,2, there are four choices. So here are all the possible pictures:

``````BB BW BG BY WB WW WG WY GB GW GG GY YB YW YG YY
``````

You can calculate this by (number of choices) raised to the (number of pixels), so in this case 4^2 = 16.

Let's say we wanted to increase the width of this picture (by making it a 1x3 image. ooh: widescreen!). For each of the original 16 pictures, you can make 4 new pictures, one for each of the color choices. So now, you have 64 pictures. Which still fits our formula: (choices)^(pixels) 4^3 = 64.

Another note: if you are dealing with x bits, the number of color choices will always be 2^x

• Kindly answer the second question – Any Jan 18 '11 at 3:39
• I think he did answer your second question. You asked for the number of images by all permutations, which implies maximum in and of itself. – user3463 Jan 18 '11 at 6:14
• What if the object changes, texture, lightning etc changes... – Any Jan 18 '11 at 6:30
• While this is clearly the answer for a bitmap image of the given requirements, I suspect JPEG's lossy compression effectively reduces this value. – DMA57361 Jan 18 '11 at 12:37
• If anyone is interested, this value works out to `8.9542950495824726607075904256630349841435477985541... × 10^2219433` ( Wolfram Alpha ). Otherwise known as "quite a lot". – DMA57361 Jan 18 '11 at 12:47