Conversion From Binary to Octal and Hexadecimal Number Systems - Lab Report Example

Introduction This paper consist of 5 tasks. In tasks 1 focus was on errors. In tasks 1.2 there was solution of problem involving conversion from binary to octal and hexadecimal number systems. In tasks 1.2 there is also a question on drawing a truth table. The other three tasks majorly involved complex number algebra. Task (LO 1.1) The number of moles () of an ideal gas are obtained using the equation , where is the pressure measured in Pascals (Pa), is the volume measured in cubic metres (m3), is the universal gas constant (8.31447JK-1mol-1), is the temperature measured in Kelvin (K) In a repeated experiment, the temperature of the gas was measured by a digital meter to the nearest Celsius. The following repeated measurements were obtained : 32C, 33C, 32C, 34C, 32C, 33C, 32C, 32C, 32C, 31C a) What is the uncertainty due to the reading error of the digital meter b) Calculate the uncertainty due to the random error of the repeated measurements (you can either use standard error = or ) c) Calculate the mean of the of the repeated measurements and round off to an appropriate number of significant figures d) Conclude on the uncertainty in the temperature measurements i.e. express in the form and explain the choice of your uncertainty , . The temperature of the gas must be in Kelvin before it is used in the equation. This is obtained by adding 273 to the Celsius temperature. The measured values of the other quantities are: Pa cm3 JK-1mol-1 e) Calculate the value of with its uncertainty given to an appropriate number of significant figures. Maximum possible value Minimum possible value Uncertainty Task (LO 1.2) 1) Convert the binary 1101 1110 1010 1101 into a) Octal Table 1 Binary Octal Deci 4 2 1 0 0 0 0 0 0 0 1 1 1 0 1 0 2 2 0 1 1 3 3 1 0 0 4 4 1 0 1 5 5 1 1 0 6 6 1 1 1 7 7 From the table1 it can be seen that you need 3 cells to represent any possible digit in octal number octal number We divide the binary numbers into 3 cells to and represent each in octal starting from left. We give each of the 3 cell binomial number its octal equivalent according to table 1. Table 2 001 101 111 010 101 101 1 5 7 2 5 5 Thus the octal number =157255 b) hexadecimal Binary Hexadecimal Decimal 8 4 2 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 2 2 0 0 1 1 3 3 0 1 0 0 4 4 0 1 0 1 5 5 0 1 1 0 6 6 0 1 1 1 7 7 1 0 0 0 8 8 1 0 0 1 9 9 1 0 1 0 A 10 1 0 1 1 B 11 1 1 0 0 C 12 1 1 0 1 D 13 1 1 1 0 E 14 1 1 1 1 F 15 From the table3 it can be seen that you need 4 cells to represent any possible digit in hexadecimal number We divide the binary numbers into 4 cells to and represent each in hexadecimal digit starting from left. We give each of the 4 cell binomial number its hexadecimal equivalent according to table 4. 1101 1110 1010 1101 D E A D Thus the hexadecimal number is DEAD 2) Draw a truth table to determine the output states at Z with all possible combinational input states at A, B, C & D. A B C D O 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 Task (LO 1.3) Two complex numbers are such that and a) Write down in rectangular (Cartesian) form. Now, find and the principal. Substituting with assigned values b) Convert and into polar form i.e. in the form rad In polar form  rad In polar form  c) Find and the principal. Now, write in rectangular (Cartesian ) form. Principal  Task (LO 1.4) Find the m complex roots of the equation using De Moivre's theorem in rectangular (Cartesian) form. Where m is given by 3 + n modulo 5 and n is your dataset number. [For example, for n=9 then n modulo 5 = 9 modulo 5 = 4. Therefore 3 + n modulo 5 = 3+4 = 7. And the question would be to find the 7 roots of ] n=2 2 modulo 5 =7 Therefore 3+nmodulo 5 =3+7=10 From De Moivre's theorem  Task (LO 1.5) The complex impedance of a circuit containing a resistor of resistance R, inductor of inductance L and a capacitor of capacitance C is given by , where and is the frequency of the alternating power supply, measured in Hertz (Hz). Find a) the impedance to an appropriate number of significant figures Making substitutions to an appropriate number of significant figures =1989.5 Conclusion The solution of all the tasks were successfully found Read More