Bachelor of Science in Information Technology (BScIT) – Semester 1/
Diploma in Information Technology (DIT) – Semester 1
BT0064 – Digital Logic
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Assignment Set – 1
Q1. Convert the following octal numbers to base 10
a. 273 Answer: 187
b. 1021 Answer: 529
Q2. What is a logic gate?
Answer: When we deal with logical circuits (as in computers), we not only need to deal with logical functions; we also need some special symbols to denote these functions in a logical diagram. There are three fundamental logical operations, from which all other functions, no matter how complex, can be derived. These functions are named and, or, and not. Each of these has a specific symbol and a clearly-defined behavior, as follows: | | The AND GateThe AND gate implements the AND function. With the gate shown to the left, both inputs must have logic 1 signals applied to them in order for the output to be a logic 1. With either input at logic 0, the output will be held to logic 0.If your browser supports the Javascript functions required for the demonstrations built into this page, you can click the buttons to the left of the AND gate drawing to change their assigned logic values, and the drawing will change to reflect the new input states. Other demonstrations on these pages will work the same way.There is no limit to the number of inputs that may be applied to an AND function, so there is no functional limit to the number of inputs an AND gate may have. However, for practical reasons, commercial AND gates are most commonly manufactured with 2, 3, or 4 inputs. A standard Integrated Circuit (IC) package contains 14 or 16 pins, for practical size and handling. A standard 14-pin package can contain four 2-input gates, three 3-input gates, or two 4-input gates, and still have room for two pins for power supply connections. | | | The OR GateThe OR gate is sort of the reverse of the AND gate. The OR function, like its verbal counterpart, allows the output to be true (logic 1) if any one or more of its inputs are true. Verbally, we might say, "If it is raining OR if I turn on the sprinkler, the lawn will be wet." Note that the lawn will still be wet if the sprinkler is on and it is also raining. This is correctly reflected by the basic OR function.In symbols, the OR function is designated with a plus sign (+). In logical diagrams, the symbol to the left designates the OR gate.As with the AND function, the OR function can have any number of inputs. However, practical commercial OR gates are mostly limited to 2, 3, and 4 inputs, as with AND gates. |
| | The NOT Gate, or InverterThe inverter is a little different from AND and OR gates in that it always has exactly one input as well as one output. Whatever logical state is applied to the input, the opposite state will appear at the output.The NOT function, as it is called, is necesasary in many applications and highly useful in others. A practical verbal application might be:The door is NOT locked = You may enterThe NOT function is denoted by a horizontal bar over the value to be inverted, as shown in the figure to the left. In some cases a single quote mark (') may also be used for this purpose: 0' = 1 and 1' = 0. For greater clarity in some logical expressions, we will use the overbar most of the time.In the inverter symbol, the triangle actually denotes only an amplifier, which in digital terms means that it "cleans up" the signal but does not change its logical sense. It is the circle at the output which denotes the logical inversion. The circle could have been placed at the input instead, and the logical meaning would still be the same. |
Q3. Minimize the following functions using Quine-McCluskey tabular method:
a.
b.
(With don’t care terms 2,7,13,22,23)
Answer:
a. F = A'B'C' + B'D + BCD' + AC + ABD'
b. F = ACD + B'CE + A'B'D'E + A'C'D'E' + AB'D'E' + BC'DE + BCE' + ABC'E
Q4. Design 2-bit comparator using gates.
Answer:
Q5. Define Sequential Circuits.
Answer: Sequential Circuits Inc. (SCI) was a California-based synthesizer company that was founded in the early 1970s by Dave Smith and sold to Yamaha Corporation in 1987. The company, throughout its lifespan, pioneered many groundbreaking technologies and design principles that are often taken for granted in today's greatly enhanced world of music technology. Sequential Circuits was also pivotal in the planning, design, and support of 1982's groundbreaking music technology.
Q6. Give any two applications of shift register.
.
Answer: In digital circuits, a shift register is a cascade of flip flops, sharing the same clock, which has the output of anyone but the last flip-flop connected to the "data" input of the next one in the chain, resulting in a circuit that shifts by one position the one-dimensional "bit array" stored in it, shifting in the data present at its input and shifting out the last bit in the array, when enabled to do so by a transition of the clock input. More generally, a shift register may be multidimensional; such that its "data in" input and stage outputs are themselves bit arrays: this is implemented simply by running several shift registers of the same bit-length in parallel.
Shift registers can have both parallel and serial inputs and outputs. These are often configured as serial-in, parallel-out (SIPO) or as parallel-in, serial-out (PISO). There are also types that have both serial and parallel input and types with serial and parallel output. There are also bi-directional shift registers which allow shifting in both directions: L→R or R→L. The serial input and last output of a shift register can also be connected together to create a circular shift register.
4-Bit SIPO Shift Register
Q7. Explain the working principle of 4 bit Johnson counter with a neat diagram.
Answer: If the output of a shift register is fed back to the input. a ring counter results. The data pattern contained within the shift register will recirculate as long as clock pulses are applied. For example, the data pattern will repeat every four clock pulses in the figure below. However, we must load a data pattern. All 0's or all 1's doesn't count. Is a continuous logic level from such a condition useful?
Q8. Explain temperature and weather forecast system with a neat circuit diagram.
Answer: The value of utilizing long-range weather predictions for making extended hydrologic forecasts has been the subject of debate among hydrologists for a long time, since these predictions are of marginal skill for significant portions of the continental United States, especially at hydrologic-relevant spatial and temporal scales. However, the interest in using monthly and seasonal temperature and precipitation outlooks for making extended hydrologic predictions has increased considerably in the past few years for two main reasons: (1) the prospect exists for improved weather forecast accuracy through enhanced ocean-atmosphere and land-surface coupled models, and (2) for a number of hydrologic applications even a small gain in forecast skill potentially leads to larger increases in their social and economic value.
The portion of the National Weather Service River Forecast System that produces probabilistic forecasts of stream flow and stream flow-related variables for periods up to 12 months was originally called Extended Stream flow Prediction (ESP) system. The original version of ESP created an ensemble of stream flow traces using multiple years of historical time series of precipitation and temperature as possible future meteorological realizations.
These traces were then analyzed statistically to make a probabilistic forecast of any stream flow-related variable. ESP was not originally configured to handle weather forecasts as input (with the exception of a deterministic short-term Precipitation forecast). During the statistical analysis ESP allowed a forecaster to assign weights to simulated stream flow traces based on his or her judgment about the similarity between the weather conditions of each historical year and the forecast for the current year. Since such weighting was subjective, it was generally not performed at all.
In order to enhance long-range hydrologic predictions through climate forecasts, a methodology was developed in the National Weather Service (NWS) to facilitate incorporation of climate outlooks into the ESP. The schematic of the new Ensemble Stream flow Prediction (ESP) system with integrated weather forecasts is given in Figure
Q9. Explain the functioning of digital multi-meter.
Answer: Click here Ans: DIGITAL MULTI-METER, also known as Digital Video Disc or Digital Versatile Disc, is an optical disc storage media format, and was invented and developed by Philips, Sony, TOSHIBA, and Time Warner in 1995. Its main uses are video and data storage. DIGITAL MULTI-METERs are of the same dimensions as compact discs (CDs), but store more than six times as much data.
Variations of the term DIGITAL MULTI-METER often indicate the way data is stored on the discs: DIGITAL MULTI-METER-ROM (read only memory) has data that can only be read and not written; DIGITAL MULTI-METER-R and DIGITAL MULTI-METER+R (recordable) can record data only once, and then function as a DIGITAL MULTI-METER-ROM; DIGITAL MULTI-METER-RW (re-writable), DIGITAL MULTI-METER+RW, and DIGITAL MULTI-METER-RAM (random access memory) can all record and erase data multiple times. The wavelength used by standard DIGITAL MULTI-METER lasers is 650 nm;[4] thus, the light has a red color.
DIGITAL MULTI-METER-Video and DIGITAL MULTI-METER-Audio discs refer to properly formatted and structured video and audio content, respectively. Other types of DIGITAL MULTI-METERs, including those with video content, may be referred to as DIGITAL MULTI-METER Data discs.
Q10. Write a short note on ADC.
Answer: Click here Ans: Basic operation
Ideally sampled signal.
A DAC converts an abstract finite-precision number (usually a fixed-point binary number) into a concrete physical quantity (e.g., a voltage or a pressure). In particular, DACs are often used to convert finite-precision time series data to a continually varying physical signal.
A typical DAC converts the abstract numbers into a concrete sequence of impulses that are then processed by a reconstruction filter using some form of interpolation to fill in data between the impulses. Other DAC methods (e.g., methods based on Delta-sigma modulation) produce a pulse-density modulated signal that can then be filtered in a similar way to produce a smoothly varying signal.
By the Nyquist–Shannon sampling theorem, sampled data can be reconstructed perfectly provided that its bandwidth meets certain requirements (e.g., a baseband signal with bandwidth less than the Nyquist frequency). However, even with an ideal reconstruction filter, digital sampling introduces quantization error that makes perfect reconstruction practically impossible. Increasing the digital resolution (i.e., increasing the number of bits used in each sample) or introducing sampling dither can reduce this error.
