Representation of an image pixel from 8bit (Binary) to Fibonacci number

We can represent a pixel of an 8-bit image as under:

Let we have a pixel whose value is 39 then its equivalent binary is

39 = 111001 = 1 × 1 + 1 × 2 + 1 × 4 + 0 × 8 + 0 × 16 + 1 × 32, which is a unique representation of number 39.

However, if we try to represent the same number (39) in Fibonacci sequence then we need 12-bit plans instead of 8-bit planes (in the case of Binary number system) and we get different sequences which can produces the number 39 as under:

39 = 011000010000 = 0×1 + 1×2 + 1×3 + 0×5 + 0×8 + 0×13 + 0×21 + 1×34 + 0×55 + 0×89 + 0×144 + 0×233, or

39 = 000100010000 = 0×1 + 0×2 + 0×3 + 1×5 + 0×8 + 0×13 + 0×21 + 1×34 + 0×55 + 0×89 + 0×144 + 0×233, or

39 = 000101100000 = 0×1 + 0×2 + 0×3 + 1×5 + 0×8 + 1×13 + 1×21 + 0×34 + 0×55 + 0×89 + 0×144 + 0×233.

Therefore, I need a Matlab code to represent a number or image pixel into different possible Fibonacci sequences. Please, anyone share.

I shall be very thankful.

Toqeer (<mailto:[e-mail] [e-mail]>)