Assuming that by "binary image" you meant a 1-bit bitmap image (an image with 1-bit per pixel).
If the two images have the same size, you can do a bitwise XOR of the two bitmaps.
The truth table for bitwise XOR operation is:
a b | o
------+---
0 0 | 0
0 1 | 1
1 0 | 1
1 1 | 0
Then you can find the number of 1s in the bitstring to get the number of pixels that changes between the two images.
Anderson's Bit Twiddling Hacks page gives several different strategies for efficiently counting the number of bits in an integer/bitset.