The July 2015 Computer and Internet Use Supplement was conducted as a supplement to that month’s CPS. The CPS is a monthly labor force survey conducted in approximately 56,000 interviewed households across the country. The ASEC is unique among the CPS files – it includes all March Basic Monthly Survey respondents as well as oversamples from other months.
The difference in N that you have between the two does not seem unusual. According to the documentation, the July 2015 Computer and Internet Use Supplement collected household information from all eligible CPS households, as well as person information from household members 3 years old and over. From this page, you can see that the number of persons you have is slightly less than the total sample size for the CPS in July 2015. Additionally, you can see the natural variability from month-to-month as well as the increased sample size for March, when the ASEC takes place.