Solutions_Midterm_Exam

# Solutions_Midterm_Exam - University of Central Florida...

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University of Central Florida School of Engineering and Computer Science Department of Computer Science CDA 3103 – Computer Organization Midterm Exam - Solutions Prof: Dr. Hassan Foroosh TA: Remo Pillat Date of submission: June, 29 th 2006

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2 0 0 0 0 0 1 1 0 00 01 11 10 0 1 10 AA 0 B 1 0 0 0 0 0 0 1 00 01 11 10 0 1 A A 0 B 0 B 1 A A B Question 1 (25 points) The following truth table corresponds to an unsigned binary multiplier that multiplies a 2-bit number by a 1-bit number 0 B and generates the product 210 PPP . (5 pts) Complete the following truth table (15 pts) Give the most simplified expressions for 0 P , and 1 P in sum-of-products form using K-maps. (5 pts) Implement 1 P using only NOR gates. Answer: The rules for multiplying a 2-bit number by a 1-bit number should be clear by now, so that the generation of the truth table is straightforward. 1 A 0 A 0 B 2 P 1 P 0 P 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1 Given the truth table, you can write down the 2 Karnaugh-Maps (one for each output 0 P and 1 P ) and deduce the minimized sum-of-products forms. 00 0 PA B = 11 0 B = For implementing 1 P with only NOR gates, DeMorgan’s Rule from Boolean Logic helps us, since: () 0 1 0 1 0 P A BA B A n o r B == = + = . We already know from the labs, that one inverter can be easily implemented with one NOR gate with doubled input:
3 Question 2 (25 points) A physical constant that plays a crucial role in quantum mechanics is the Planck’s constant, which is roughly equal to 118 220.2 2 hJ s . (15 pts) What is the representation of Planck’s constant in single precision IEEE-754 format? (10 pts) In some scientific computation your program has to multiply the following number by Planck’s constant: 0111 1001 0110 0000 0000 0000 0000 0000 M = What is the binary representation of the resulting number in single precision floating point if we use their normalized representation for multiplication? Answer: First we have to convert the decimal number 220.2 into binary format. To convert 220 we use the division- by-2 method and for 0.2 the multiply-by-2 method. The resulting binary number 118 11011100.0011 2 × has to be normalized to the scientific notation. Hence 118 111 11011100.0011 2 1.10111000011 2 −− ×= × The 32 bits of the floating point number are divided into three parts that are determined as follows: Sign Bit= 0 (Positive Number) Exponent= 0001 0000 (=-111+127=16) Mantissa= 1.1011 1000 0110 0110 0110 011 0 0001 0000 101 1100 0011 0011 0011 0011 18 23 0 31 CONVERTING RESULT 220 2 110 ÷= 0 110 2 55 00 55 2 27 100 27 2 13 1100 13 2 6 11100 623 011100 321 1011100 12 0 11011100

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## This note was uploaded on 08/22/2010 for the course CDA 3101 taught by Professor Staff during the Fall '07 term at University of Central Florida.

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Solutions_Midterm_Exam - University of Central Florida...

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