Review Problems and Solutions - Review Problems and...

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Review Problems and Solutions (For Chapters 1 and 2) 1. Suppose that a computer memory has a capacity of 512K bytes. Furthermore, suppose that each memory cell can contain 2 bytes of information. How many Hex digits are necessary to represent all of the memory addresses? Answer: First we need to determine how many memory cells there are. Since total capacity is 512K bytes and each cell contains 2 bytes, there are: 512K bytes / 2 bytes per cell = 256K cells Now, 256 is 2 to the power 8 (written as 2^8) and 1K = 2^10, so 256K is equivalent to 2^18. Since there are 2^18 cells, we need a total of 18 bits to represent all memory addresses in binary. Each group of 4 bits can be represented using 1 Hex digit. So out of the 18 bits for a memory address the right-most 16 bits can be represented using 4 Hex digits. We will also need an additional Hex digit to represent the left-most 2 bits (using 2 leading 0's). So together we need 5 Hex digits. For example, consider the memory address 111011000111001001 which is 18 bits. Adding the leading two 0's and separating into groups of 4 bits gives us the following (included below each 4 bits is their shorthand the Hex digit): 0011 1011 0001 1100 1001 3 B 1 C 9 2. For what input combinations of X and Y is the output of the following combination circuit a 1? 3. _____ 4. X >----| | _____ 5. | XOR |------| | 6. Y >-+--|_____| | AND |---> output 7. | +--|_____| 8. | | 9. | _____ | 10. | | | | 11. +--| NOT |o--+ 12. |_____| Answer: First look at the AND gate. The output of the circuit is the output of the AND gate. For this output to be a 1, both inputs to the AND must be 1's. So the outputs of the XOR gate as well as the NOT gate must be 1's. For the NOT gate, this means that the input Y must be a 0. Now what should be the input to XOR? We already know Y has to be a 0. So, for XOR to produce a 1, the input X must be different from Y. In other words, X must be a 1. So the answer is that for X=1 and Y=0, the circuit will produce a 1. In this case no other combination of X and Y will produce a 1. Just for completeness, let's look at the output of the circuit for all possible combinations of X and Y. This is summarized in the following "truth table": X Y output -----------------------
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0 0 0 0 1 0 1 0 1 1 1 0 13. Perform the following additions in 2's complement and indicate if there is an error:
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Review Problems and Solutions - Review Problems and...

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