How to calculate address range of memory chips
For this, you need to see the 74LS244 and 74LS138 datasheets and work out which combinations of A15...A19 give chip selects to which chip. Each 62256 has 256 kilobits,
which is 32 kilobytes.

So, First you think that A[19:15] = '00000'. That's the first 32KB memory block. Trace the states of the 74LS244 outputs for that combination. Then trace the outputs of the 74LS138's for that combination. The memory chip that gets a '0' in its chip select is activated for that memory region. Then continue from there, you'll soon figure it out.