# Digital Logic and Data Manipulation Coursework - Section B

Added on 2019-09-19

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DIGITAL LOGIC AND DATA MANIPULATION COURSEWORK - SECTION BQuestion 1Modern-day digital computers can run complex applications, and that too in a small form and by consuming less power as compared to earlier generations of computers (DeMone, 2004). This has been enabled by the decision to basemodern electronics internal working on binary number systems (Blinnikov, 2010). Now, we explore why binary number system is used for modern-day digital computers and not any other say decimal (base 10), octal (base 8), hexadecimal (base 16) or any other arbitrary number-system base.Ease of Design / Manufacture / Low CostsIt is easier to design a computer's internal system when we are dealing with the minimum number of discrete states (Saha and Mukherjee, 2016) and two is the lowest base number that can satisfy the mathematical requirements from a digital computer (cs.stackexchange.com, 2014). This is confirmed by Kjell, (n.d.) that binary is simple and easy to build, and it is this simplicity also allows us to easily combine components into sophisticated systems (Harris and Harris, 2015). This also reflects in cheaper manufacture and lower costs (Clements, 2006).Low Power ConsumptionEvery state to be represented in a digital circuit will require a separate band ofvoltage, thus more states (e.g. ten states in decimal system) will require ten separate voltage bands and thus will consume more power. And as per N (n.d.) we do not see any gains for a digital computer by increasing the numberof states, so there is no reason to have a higher-consumption circuit. Noise Immunity / Reliability <Your Name> <Your Student Number> 20161 of 7

The physical circuits may be using discrete logic (binary or any other), but they are still using analog signals (electricity) to work. Analog signals move from one value to another smoothly and not abruptly. Thus, we need gaps or steps around the chosen voltage bands to unambiguously identify the state being represented. An additional impetus for reducing the number of states is the fact that electronic signals are not always very steady and can vary because of surrounding influences N (n.d.). Thus, the circuits are much more reliable when only two states are concerned. Compatibility With Other HardwareIn addition, most hardware used along with a computer is bi-state i.e. having either of the two states possible On or Off e.g. (magnetic) hard disks' elemental storage unit can be magnetised (On) or not magnetised (Off); an optical disk (DVD, CD)'s elemental storage unit can reflect a light or not reflecta light to indicate the two states possible; a fiber optic cable can send a pulse of light (On) or not send any light i.e. darkness (Off) to indicate the two states possible.Question 2For the given scenario of proposed car's ignition system, we have two variables to consider - starting the ignition (say start position, SP) and pressing of clutch (say clutch position, CP). Both of these variables are binary,with the states mentioned below:SP: 1 = starting the ignition, 0 = ignition is off, or the engine is runningCP: 1 = clutch is depressed, 0 = clutch is not pressed i.e. normal positionNow, number of possibilities in any number system is given by (base)number of variables. So we have (base of binary)number of variables in the given scenario possibilities i.e. 22 = 4 possible states, which are indicated along with the desired operation in the following Truth Table:InputsOutput (Q) <Your Name> <Your Student Number> 20162 of 7

CPSPQ0 = Do not startengine,1 = Start engineClutch Position (CP)Start Position (SP)000010100111Thus, we see that we have action (truth value) only in one scenario for which both the inputs are true. This seems like a good case for AND operation. Thus, the Boolean expression for this scenario becomes:Output = CP . SPAnd, finally the logic diagram becomes:Question 3We will redesign the system used at Rockledge Corporation to monitor five parameters at once and walk-through the process. The system is used to automatically ensure safety measures in industrial plant operations. There area couple of physical parameters like temperature, pressure, etc. which must be monitored and if either of them exceeds the threshold of safety, then the plant must shut down. <Your Name> <Your Student Number> 20163 of 7

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