Solutions_Midterm_Exam

Solutions_Midterm_Exam - University of Central Florida...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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:
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 10

Solutions_Midterm_Exam - University of Central Florida...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online