Quantisation for IMAGE COMPRESSION

I'm doing an image compression using discrete cosine transform project....(To be implemented in hardware using Fixed Point Arithmetics)

DCT=(c)(x)(cT) c cosine coefficients... x image.... cT represent cosine transpose....

how can i check the error if i'm using 8 bits to represent the cosine matrix and the cosine transpose? eg: Also, suppose if i'm multipling two 8 bit numbers( each of them has 5 bit for decimal part and 3 bit for fractional part) then the result will be naturally 16 bits( ie. 10 bit decimal part plus 6 bit fraction part)

If i quantize the result by represending with say 12 bits....now what will be the error ............?how can i find it?Does matlab has an inbuilt function for this?

can anyone explain how this can be done.........