This is a close-book exam. Calculator is allowed. Your answer should be given in the exampapers immediately following the questions.1. Binary-to-decimalConvert 00111 to decimal?2. Decimal-to-binaryConvert 49 to binary?3. ASCII tableWhat is the decimal number of character "B" in ASCII table? What is the binary number of "B"?4. Logic Gates and Logic TablesIn the image below, four NANDS are connected and three of the inputs are set to 1. What are the values of Z if B = 1 and A = 0? For reference, the logic table associated with a NAND gateis shown.A. Z=0, output=0B. Z=0, output=1C. Z=1, output=0D: Z=1, output=1E: can not be determined5. Sensor: Analog to Digital ConverterIn a 7 bit analog to digital converter, how many different levels of data can be recorded?A. 7B. 70C. 128D. 256E. 10246. Sensor: resolutionA scientific temperature sensors has an operational range between -200 and 200 degree in Fahrenheit, and use 12 bits to convert the data. What is the temperature resolution of the detector?7. IterationConsidering the following iteration code, what is A(12)?---------------------------------------------------------------------The following statement is used for question 8, 9, 10, 11-------------------------------------------------------------------------8. Scientific Model to Mathematical ModelTranslate the above statement into a mathematical representation9. Mathematical Model to Computational ModelTranslate your mathematical representation into Matlab/Octave code that uses iteration to specify your balance after 10 years.10. Interval and sub-intervalWhen you are asked to calculate the balance for the next 10 years on a yearly basis. What is the interval and sub-interval of the calculation?11. What is the balance in the 4th year?12. Differentiation equationTranslate the following differential equation into the iteration mathematical representation13. IntegrationConsider the integration of the function, f(x)=x, from the interval of x=0 to x=4.0. You are asked to make a numerical approximation of this integration using the area method, that is to find the geometric area underneath the function with the sum of a series of rectangles.If you choose the sub-interval Δx=1.0, what is the approximated area?14. If the sub-interval is chosen to be Δx=0.1, do you think that you will get a different value of the numerical integration? Explain why?15. Validation: scientific methodDescribe in a few sentences in your word what is a scientific method?CDS 130-003 Computing for ScientistsMidterm Exam ReviewOct. 21, 2010TopicsSession 1: FundamentalsCH1: Binary Representation- Binary to decimal conversion: power method- Decimal to binary conversion: long division methodCH2: Data Storage- Data density- Bits and bytes- ASCII table, encodingCH3: Logic Circuits and Logic Tables- Transistor: the building block- AND gate, AND table; OR gate, OR table; NOT gate, NOT table- NAND gate, NAND table- XOR (EOR) gate, XOR table- Adding binary numberSession 2: MeasurementsCH1: Sensors- Electric measurement- CCD (Charge Coupled Device)CH2: Sensor Limitations- Lower limit and upper limit- Resolutions: Time, Space, and Level- ADC: Analog to Digital Converter- Signal, noise and background- Signal to Noise Ration (SNR)Session 3: Scientific SimulationCH1: Mathematical model- Scientific model to mathematic modelCH2: Numerical method- Iteration- Differential equation- Interval and sub-interval- Integration- Integration accuracy and size of sub-interval (or number of iteration)CH3: Verification and Validation- Scientific method: characterization, hypothesis, prediction and testing-Sample Midterm Exam (2010 Oct)This is a close-book exam. Calculator is allowed. Your answer should be given in the exampapers immediately following the questions. 1. Binary-to-decimal Convert 00111 to decimal?2. Decimal-to-binary Convert 49 to binary? 3. ASCII table What is the decimal number of character "B" in ASCII table? What is the binary number of "B"?4. Logic Gates and Logic TablesIn the image below, four NANDS are connected and three of the inputs are set to 1. What are the values of Z if B = 1 and A = 0? For reference, the logic table associated with a NAND gate is shown. A. Z=0, output=0B. Z=0, output=1C. Z=1, output=0D: Z=1, output=1E: can not be determined5. Sensor: Analog to Digital ConverterIn a 7 bit analog to digital converter, how many different levels of data can be recorded?A. 7B. 70C. 128D. 256E. 10246. Sensor: resolutionA scientific temperature sensors has an operational range between -200 and 200 degree in Fahrenheit, and use 12 bits to convert the data. What is the temperature resolution of the detector?7. IterationConsidering the following iteration code, what is A(12)?---------------------------------------------------------------------The following statement is used for question 8, 9, 10, 11-------------------------------------------------------------------------8. Scientific Model to Mathematical ModelTranslate the above statement into a mathematical representation9. Mathematical Model to Computational ModelTranslate your mathematical representation into Matlab/Octave code that uses iteration to specify your balance after 10 years.10. Interval and sub-intervalWhen you are asked to calculate the balance for the next 10 years on a yearly basis. What is the interval and sub-interval of the calculation? 11. What is the balance in the 4th year?12. Differentiation equationA(9)=13;for i=[10:12] A(i)=A(i-1)+37;endMy bank offers 5% interest on my account compounded yearly. Every year I deposit an additional $100. Assuming that on the first year your account had a balance of $100.Translate the following differential equation into the iteration mathematical representation dPdt=0 .5×P13. IntegrationConsider the integration of the function, f(x)=x, from the interval of x=0 to x=4.0. You are asked to make a numerical approximation of this integration using the area method, that is to find the geometric area underneath the function with the sum of a series of rectangles. If you choose the sub-interval Δx=1.0, what is the approximated area? 14. If the sub-interval is chosen to be Δx=0.1, do you think that you will get a different value of the numerical integration? Explain why? 15. Validation: scientific methodDescribe in a few sentences in your word what is a scientific method? f (x )=xF=∫04 . 0xdxInformation Sheet1. ASCII Table2. NAND gate and its logic