Step 1: Understanding memory units
Memory sizes in computing follow a binary multiple system. The common memory units in increasing order are:
Kilobyte (KB) = $2^{10}$ bytes
Megabyte (MB) = $2^{20}$ bytes
Gigabyte (GB) = $2^{30}$ bytes
Terabyte (TB) = $2^{40}$ bytes
Step 2: Evaluate the options
Option (1) presents the correct ascending order: KB < MB < GB < TB.
Other options mix up the order incorrectly.
Step 3: Conclusion
The correct increasing order of memory sizes is: KB, MB, GB, TB.