# CDA 3103 Computer Organization Exam 1 (Sep. 22th, 2014)

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1 CDA 3103 Computer Organization Exam 1 (Sep. 22th, 2014) Name: USF ID: Problem Points Score otal 80 Exam Rules Use the back of the exam paper as necessary. But indicate clearly which problems that the answers on the back correspond to. Make sure that your writing is legible; otherwise you grades may be adversely affected. Close book, notes and HW. Except the quiz paper, one cheating sheet double side is allowed in A4 or Letter. All electronics must be turned off. Show all work to get partial credits except yes/no problems.

2 Problem 1 (10 points): Answer true () or false (F) to each of the following questions. Omit this question and everyone gets 1 point both have two representations for zero. Signed-magnitude and two's complement F he even parity is used for the code word ( ) 2. he range of decimal values that can be expressed in n bits using binary two's complement is to. F F out. Every hexadecimal number corresponds to a unique binary number. he Boolean OR operation is also known as Boolean product. Signed-magnitude and two's complement both have two representations for zero. Von Neumann computers execute instructions sequentially. Overflow is indicated when the carry in to the high-order bit is not equal to the carry Boolean simplication allows to produce a smaller or faster digital circuit. GHz is often used to measure the clock speed of a computer. Problem 2 (10 Points). Multiple Choice and short answers 1) he level of the computer hierarchy where an operating system functions is the C. A) control level B) machine level C) system software level D) digital logic level 2) here are B megabytes in a terabyte. A) B) C) D) 3) he Boolean AND operation is also known as B : A) Boolean sum B) Boolean product C) the complement of a Boolean OR D) the complement of a Boolean XOR

3 4) he Boolean function F(x, y, z) = y(x'z + xz) + x'yz' + xy'z simplifies to: A A) xz + x'y B) x'z + xy C) x'z + xyz D) xy + x'z 5) Which of the following equations correctly reflects the truth table shown below C? x y z F A) (xy'z + x'yz' + x'yz' + x'y'z + x'y'z)' B) xy'z + x'yz' + x'yz' + x'y'z + x'y'z C) x'yz' + x'yz + xy'z' + xyz' + xyz D) (x'yz' + x'yz + xy'z' + xyz' + xyz)' 6) he truth table shown below is supposed to reflect the function F(x, y, z) = y(x + z') but two lines are in error. Identify them. B A) 1 and 2 B) 3 and 4 C) 5 and 6 D) 7 and 8 # x y z F ) he Boolean function F(x, y) = x'y + xy' + (x'+y')(xy) can be simplified to: B

4 A) x'y' B) x y C) xy D) 1 8) 01AF (base 16) = 431 (base 10) 9) Convert 0B2C (base 16) to binary ) Convert to binary with 8 bits to the right of the binary point Problem 3 (15 pts): he following table shows five binary numbers in column Binary. he first column in the table shows IDs referring to the corresponding binary numbers in column Binary. Assume only 8 bits are used. Use the ID numbers in the first column to answer the following questions when necessary. 1. Find the hexadecimal representation for the binary number in the same row by filling the blanks in column Hexadecimal in the above table. Answer: 0xFF, 0x07, 0xF8, 0x87, 0x80 2. Which of the above binary numbers has the largest decimal value if it represents an unsigned integer? Ans: n1 3. Which of the above binary numbers has the same decimal value if it is treated as the signed-magnitude, 1's complement or 2's complement representation? Ans: n2 4. Which of the above binary number has the largest decimal value if it is in 2's complement representation? Ans: n2 5. Which of the above binary number has the smallest decimal value if it is in 2's complement representation? Ans: n5

5 Problem 4 (15 Points). Complete the following two operations using two's complement arithmetic with 8 bits. Verify if the results are correct. If not, give a brief explanation. 1) ) ) First, find the 2's complement binary numbers for 11: : (carry) he result is incorrect. he sum of two positive numbers get negative output. his is due to the overflow. Use the rule of overflow. 2) First, find the 2's complement binary numbers for 11 : : (carry) he result corresponds the decimal value -110, which is correct. Problem 5 (10 pts) write a simplified expression for the Boolean function using Kmaps. yz wx Ans: wy +y z+w xy+x yz

6 Problem 6 (20 pts): Show that a) (10pts) Using truth table b) (10pts) Using Boolean identities. Show all intermediate steps and identity used to get full credits.

7 Boolean Identities

8 his page is intentionally left blank. You can use it as work sheet.

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