The IBM 370 mainframe computer was introduced in 1970. The 370 Model 145 could hold up to 524,288 bytes of data (512 Kbytes). It cost $1,783,000.00 to buy (or $37,330/month to rent). A notebook computer today holds 16 Gbytes of memory and costs $2,500 to buy. If you assume that 100% of the price is just the memory, for both computers:

• how much did 1 Kbyte of memory in the IBM computer cost?

• how much does 1 Kbyte of memory in the laptop cost?

• how many times cheaper is the memory in the laptop than memory in the mainframe?

• what factor is today's computer cheaper than the IBM 370?

a) $3482.4 per Kbyte

b) $0.000149 per Kbyte

c) The laptop is 23369991 times cheaper than the mainframe computer

d) Today's computer is 23369991 times cheaper than IBM 370

Explanation:

a) The 370 Model 145 could hold up to 524,288 bytes of data

one Kb = 1024 bytes, therefore 524,288 bytes = 524288/1024 Kbytes = 512 Kbytes. It cost $1,783,000.00 to buy (or $37,330/month to rent).

Since 100% of the price is just the memory

Cost per 1 Kb = cost of computer / memory

Cost per 1 Kb = $1,783,000 / 512 Kb = $3482.4 per Kbyte

b) A notebook computer today holds 16 Gbytes of memory

one Kb = 1024 bytes, 1024 Kb = 1 Mbyte, 1024 Mbytes = 1 Gbyte.

Therefore 16 Gbytes = (16 * 1024 * 1024) Kbytes = 16777216 Kbytes. It cost $2500 to buy

Since 100% of the price is just the memory

Cost per 1 Kb = cost of computer / memory

Cost per 1 Kb = $2500 / 16777216 Kb = $0.000149 per Kbyte

c) Cost per 1 Kb for mainframe / Cost per 1 Kb for laptop = $3482.4 per Kbyte / $0.000149 per Kbyte = 23369991

The laptop is 23369991 times cheaper than the mainframe computer

d) Today's computer is 23369991 times cheaper than IBM 370