Offsets can range in value from 0 to 65535 so it would appear that there are 65536 possible logical addresses, assuming that none require a segment outside of the valid range. This is not quite the case since the segment must be an integer. According to equation (3), we have : S=(P-O)>>4. In order for S to come out as an integer, P - O must be a multiple of 16. This means that one must divide 65536 by 16 to get the number of offsets that yield a valid segment (which is 4096). Now, we just have to check that the range restrictions are not violated. The smallest possible offset for physical address 179b8 is 8. This yields a segment of 179B (which is not too large or too small). The largest possible offset is FFF8. This yields a segment of 079C (which is also not too large or too small). Since The both the largest possible offset and the smallest possible offset yield a segment between 0 and FFFF, all the offsets in between will as well. Therefore, we can conclude that there are 4096 distinct logical addresses that can refer to physical address 179b8.