# DIGITAL LOGIC AND DATA MANIPULATION COURSEWORK - SECTION B.

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DIGITAL LOGIC AND DATA MANIPULATION COURSEWORK - SECTION BQuestion 1Modern-day digital computers can run complex applications, and that too in asmall form and by consuming less power as compared to earlier generationsof 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 digitalcomputers 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 withthe minimum number of discrete states (Saha and Mukherjee, 2016) and twois the lowest base number that can satisfy the mathematical requirementsfrom a digital computer (cs.stackexchange.com, 2014). This is confirmed byKjell, (n.d.) that binary is simple and easy to build, and it is this simplicity alsoallows us to easily combine components into sophisticated systems (Harrisand 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 tenseparate voltage bands and thus will consume more power. And as perN(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> 20161of7

The physical circuits may be using discrete logic (binary or any other), butthey are still using analog signals (electricity) to work. Analog signals movefrom one value to another smoothly and not abruptly. Thus, we need gaps orsteps around the chosen voltage bands to unambiguously identify the statebeing represented. An additional impetus for reducing the number of states isthe fact that electronic signals are not always very steady and can varybecause of surrounding influencesN (n.d.). Thus, the circuits are much morereliablewhen only two states are concerned.Compatibility With Other HardwareIn addition, most hardware used along with a computer is bi-state i.e. havingeither of the two states possible On or Off e.g. (magnetic) hard disks'elemental storage unit can be magnetised (On) or not magnetised (Off); anoptical 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 pulseof light (On) or not send any light i.e. darkness (Off) to indicate the two statespossible.Question 2For the given scenario of proposed car's ignition system, we have twovariables to consider - starting the ignition (say start position, SP) andpressing 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 ofvariables. So we have (base of binary)number of variablesin the given scenariopossibilities i.e. 22= 4 possible states, which are indicated along with thedesired operation in the following Truth Table:InputsOutput (Q)<Your Name> <Your Student Number> 20162of7

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 whichboth 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 fiveparameters at once and walk-through the process. The system is used toautomatically ensure safety measures in industrial plant operations. There area couple of physical parameters like temperature, pressure, etc. which mustbe monitored and if either of them exceeds the threshold of safety, then theplant must shut down.<Your Name> <Your Student Number> 20163of7