form chapter 2 and 3 Problem 1. How much memory space is needed to support a gen

Question

form chapter 2 and 3

Problem 1. How much memory space is needed to support a general one-to-one mapping between 8-bit input values and 8-bit output values? How about 80-bit input and output values?

Problem 2. Token cards display a number that changes periodically, perhaps every minute. Each such device has a unique secret key that is known only to a server. When a human needs to log in the server, the person must enter the displayed number to prove his/her possession of the card. How do you design such as device?

Explanation / Answer

Problem 1 : 8-bit input value means that there are total 2^8 = 256 possible inputs and similarly, 256 posible outputs . Hence, one of the 256 inputs will be mapped to one of the 256 outputs. Hence, total data = 256+256 = 512 words of 8 bits width each

Hence total memory required = 512 X 8 bits = 4096 bits = 4 Kb

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