# Midterm Exam Logism Solved

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1. [8 Points] Perform the following operations and conversions:
1. (10 1101.0101)2 + (1111 0000)2 = _____________ (base 10)
 b) (ABC.123)16 + (E0.4EE)16 = _____________ (base 16) c) (7831.75)10 + (F1F.A01)16 = _____________ (base 2) d) (10 1001 0100.11)2 + (11.25)10 = _____________ (base 16)

1. [10 Points] A newly discovered archive of music recorded by DJ Marie is to be cataloged. Each recording falls into one of four unique categories: Solo (99 items), with the Data Representers (229 items), with Boole Al-Jabr (79 items), and with the Memory Managers (92 items).
1. Suppose you must code each item in the archive without considering categories. How many bits are required to represent each item in the entire archive with a unique binary code using the least number of bits?
2. Suppose you are required to code the category of each item explicitly, as well as a number, to identify that item within the category. How many bits are needed to represent each item with a unique binary code using the least number of bits? How could one tell an item’s category by looking at the code?
3. Explain briefly why the results of parts a) and b) are different, as well as the advantages/disadvantages of both representations.

1. [4 Points] Decode the following ASCII message. Each character in ASCII is represented by a 7-bit binary code, where the most significant bit is always 0, so only the last 7 bits are used to represent the character.

00110101 00110100 00111000 00110100

1. [8 Points] The number 15, when represented as an unsigned integer with 4 bits, is 1111.
1. When represented as signed magnitude, the number X is 1111. What is X?
2. When represented as 1’s complement, the number X is 1111. What is X?
3. When represented as 2’s complement, the number X is 1111. What is X?
4. When represented as Excess-7, the number X is 1111. What is X?

1. [15 Points] Consider the following truth table that defines inputs X0, X1, and X2 and outputs Y0 and Y1.
1. Write Boolean expressions for the outputs, Y0 and Y1 in terms of the inputs, X0, X1, and X2.
2. Using the Logisim simulator, draw the logic circuit diagram that implements the Boolean expressions obtained in part (a). Add your name and email address as part of the drawing and label the inputs and output appropriately.

Don’t forget to submit your circuit file with the file name lastname_firstname_MT.circ when you submit your answers pdf file.

1. [4 Points] Suppose that a 4M x 16 main memory is built using 512K × 8 RAM chips, and memory is word addressable.
1. How many RAM chips are necessary?
2. How many address bits are needed for each RAM chip?

1. [4 Points] How many 256 x 8 RAM chips are required to provide 8192 bytes of memory? How many bits will each address contain?

1. [2 Points] Write the assembly language equivalent of the following MARIE machine language instruction:

0010 1111 1110 0100

1. [10 Points] Write the following code segment in MARIE’s assembly language:

1. [5 Points] What does the following MARIE program do? What is the value in the AC (hex) when the program halts?

1. [5 Points] A nonpipelined system takes 300ns to process a task. However, the same task can be processed in a 5-segment pipeline with a clock cycle of 60ns. Determine the speedup ratio of the pipeline for 100 tasks.

1. [5 points] Suppose a computer has 16-bit instructions. The instruction set consists of 32 different operations. All instructions have an opcode and two address fields (allowing for two addresses). The first of these addresses must be a register, and the second must be a memory. Expanding opcodes are not used. The machine has 16 registers. What is the maximum allowable size for memory?

1. [5 Points] Suppose a computer’s memory is as follows (address 100 contains the hex value CA, etc.). Assume also that these four memory locations hold one 32-bit integer. What integer value is this on a little endian machine?

1. [5 points] Suppose a byte-addressable computer using set associative cache has 224 bytes of main memory and a cache of 128 blocks, where each cache block contains 32 bytes. If this cache is 4-way set associative, what is the format of a memory address as seen by the cache?

1. [5 Points] Suppose the cache access time is 10ns, main memory access time is 200ns, and the cache hit rate is 90%. Assuming parallel (overlapped) access, what is the average access time for the processor to access an item?

1. [5 Points] Define virtual memory briefly and note its key strengths. For example, when is using Virtual Memory faster than not doing so? Can it be slower? If yes, then in which circumstances?
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