# Digital Circuits. Frequently Asked Questions

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1 Digital Circuits Frequently Asked Questions Module 1: Digital & Analog Signals 1. What is a signal? Signals carry information and are defined as any physical quantity that varies with time, space, or any other independent variable. 2. What is a system? A system can be defined as a physical device that performs an operation on a signal. 3. What are discrete time signals? Discrete-time signals are defined only on a discrete set of times. 4. What are continuous time signals? Continuous-time signals are often referred to as continuous signals even when the signal functions are not continuous; an example is a square-wave signal. 5. What are digital and analog signals? Digital signals are discrete-valued and analog signals are continuous electrical signals that vary in time 6. What are the advantages of digital signals? The usual advantages of digital circuits when compared to analog circuits are: Noise Margin (resistance to noise/robustness) Error Correction and Detection Easily Programmable Cheap Electronic Circuits Module 2: Number System 7. What is a number system? Number systems provide the basis for all operations in information processing systems. In a number system the information is divided into a group of symbols; for example, 26 English letters, 10 decimal digits etc. In conventional arithmetic, a number system based upon ten units (0 to 9) is used. However, arithmetic and logic circuits used in computers and other digital systems operate with only 0's and 1's because it is very difficult to design circuits that require ten distinct states. Page 1 of 12

2 8. What is a binary system? The number system with the basic symbols 0 and 1 is called binary. ie. A binary system uses just two discrete values. 9. What is a bit? The binary digit (either 0 or 1) is called a bit. 10. What is a symbol? A group of bits which is used to represent the discrete elements of information is a symbol. 11. What is a binary code? The mapping of symbols to a binary value is known a binary code. 12. What do you mean by positional number representation? The decimal number system uses positional number representation, which means that the value of each digit is determined by its position in a number. 13. What is a base? The base, also called the radix of a number system is the number of symbols that the system contains. The decimal system has ten symbols: 0,1,2,3,4,5,6,7,8,9. In other words, it has a base of What is a binary number? The binary number has a radix of 2. As r = 2, only two digits are needed, and these are 0 and 1. Like the decimal system, binary is a positional system, except that each bit position corresponds to a power of 2 instead of a power of 10. In digital systems, 15. How to form a decimal value of a binary number? The decimal value of a binary number can be formed by multiplying each power of 2 by either 1 or 0 followed by adding the values together. Example : The decimal equivalent of the binary number N = = 1 x x x x x x 2 0 = 43 Page 2 of 12

3 16. What is an Octal number? Octal systems use a base or radix of 8. Thus it has digits from 0 to 7 (r-1). As in the decimal and binary systems, the positional valued of each digit in a sequence of numbers is fixed. Each position in an octal number is a power of 8, and each position is 8 times more significant than the previous position. Example : The decimal equivalent of the octal number N = = 1 x x x 8 1 = What is a hexadecimal numbering system? The hexadecimal numbering system has a base of 16. There are 16 symbols. The decimal digits 0 to 9 are used as the first ten digits as in the decimal system, followed by the letters A, B, C, D, E and F, which represent the values 10, 11,12,13,14 and 15 respectively. 18. Show the relationship between decimal, binary, octal and hexadecimal number systems. Page 3 of 12

4 19. What is a Byte? A computer memory stores a large number of words, each of which is a standard size collection of bits. An 8-bit word is known as a Byte. 20. What are the properties of 2 s Compliment numbers? X plus the complement of X equals 0. There is one unique 0. Positive numbers have 0 as their leading bit ( MSB ); while negatives have 1 as their MSB. The range for an n-bit binary number in 2's complement representation is from -2 (n-1) to 2 (n-1) - 1 The complement of the complement of a number is the original number. Subtraction is done by addition to the 2's complement of the number. Module 3: Number Base Conversion 21. How to perform conversion of numbers from one number system to another? Radix Divide and Multiply Method is generally used for conversion. 22. What is a general procedure for the operation of converting a decimal number to a number in base r? There is a general procedure for the operation of converting a decimal number to a number in base r. If the number includes a radix point, it is necessary to separate the number into an integer part and a fraction part, since each part must be converted differently. The conversion of a decimal integer to a number in base r is done by dividing the number and all successive quotients by r and accumulating the remainders. The conversion of a decimal fraction is done by repeated multiplication by r and the integers are accumulated instead of remainders. Integer part - repeated divisions by r yield LSD to MSD Fractional part - repeated multiplications by r yield MSD to LSD Example: Conversion of decimal 23 to binary is by divide decimal value by 2 (the base) until the value is 0 Page 4 of 12

5 Divide number by 2; keep track of remainder; repeat with dividend equal to quotient until zero; first remainder is binary LSB and last is MSB. The conversion from decimal integers to any base-r system is similar to this above example, except that division is done by r instead of What is the procedure for converting a binary number to octal? Group the number of bits into 3's starting at least significant symbol. If the number of bits is not evenly divisible by 3, then add 0's at the most significant end. Write the corresponding 1 octal digit for each group 24. What is the procedure for converting a binary number to hexadecimal? Group the number of bits into 4's starting at least significant symbol. If the number of bits is not evenly divisible by 4, then add 0's at the most significant end. Write the corresponding 1 hex digit for each group 25. What is the procedure for converting a hexadecimal to octal? The hex to octal conversion can be carried out in 2 steps; first the hex to binary followed by the binary to octal. 26. What is the procedure for converting a decimal number to hexadecimal? Decimal to hex conversion is completed in 2 steps; first the decimal to binary and from binary to hex Page 5 of 12

6 Module 4: Boolean Algebra & Basic Operators 27. What do you mean by Switching Algebra? Due to historical reasons, digital circuits are called switching circuits, digital circuit functions are called switching functions and the algebra is called switching algebra. 28. What is a set? A set is a collection of objects (or elements) and for example a set Z {0, 1} means that Z is a set containing two elements distinguished by the symbols 0 and What are the three primary operations? There are three primary operations AND, OR and NOT. 30. What is the precedence of evaluation in switching algebra? Like standard algebra, switching algebra operators have a precedence of evaluation. The following rules are useful in this regard. 1. NOT operations have the highest precedence 2. AND operations are next 3. OR operations are lowest 4. Parentheses explicitly define the order of operator evaluation and it is a good practice to use parentheses especially for situations which can cases doubt. Module 5: Additional Logic Operations 31. What is a NAND operation? NAND (NOT - AND ) is the complement of the AND operation 32. What is a NOR operation? NOR (NOT - OR) is the complement of the OR operation 33. What is a XOR operation? Exclusive OR is similar to the inclusive OR except output is 0 for 1. It is stated in other words as the output is 1 when modulo 2 input sum is equal to What is a XNOR operation? Exclusive NOR is the complement of the XOR operation. Alternatively the output is 1 when modulo 2 input sum is not equal to What are the three different output stages of tri state buffer? This circuit is so-called tri-state because it has three output states: high (1), low (0), and high impedance (Z) Page 6 of 12

7 Module 6: Analyses and Synthesis of Combinational Logic Circuits 36. What is a logic expression? A mathematical formula consisting of logical operators and variables. 37. What is a logic operator? A function that gives a well-defined output according to switching algebra. 38. What is a logic variable? A symbol representing the two possible switching algebra values of 0 and What is a logic literal? The values 0 and 1 or a logic variable or it's complement. 40. What do you mean by Literal Analysis? Literal analysis is process of manually assigning a set of values to the inputs, tracing the results, and recording the output values. For 'n'' inputs there are 2n possible input combinations. From input values, gate outputs are evaluated to form next set of gate inputs and evaluation continues until gate outputs are circuit outputs. The literal analysis only gives us the truth table. 41. What do you mean by Symbolic Analysis? Symbolic analysis also starts with the circuit diagram like literal analysis. But instead of assigning values, gate output expressions are determined. Intermediate expressions are combined in following gates to form complex expressions. Symbolic analysis is more work but gives us complete information of both the truth table and logic expression. 42. What do you mean by minterm? A binary variable may be either in its true form A or its complement. For n variables, the maximum number of input variable combinations is given by N = 2 n. Then considering the AND gate, each of the N logic expressions formed is called a standard product or minterm. 43. What do you mean by maxterm? Similar to minterm, if we consider an OR gate, each of the N logic expressions formed is called a standard sum or maxterm. 44. What is a SOP expression? The SOP expression is the equation of the logic function as read off the truth table to specify the input combinations when the output is a logical What is a POS expression? The POS expression is the equation of the logic function as read off the truth table to specify the input combinations when the output is a logical 0. Page 7 of 12

8 Module 7: Logic Expression Minimisation 46. What are the three main logic expression minimisation methods? Algebraic minimization, Karnaugh Map minimization and Quine-McCluskey (tabular) minimization 47. What is an algebraic minimisation process? The algebraic minimization process is the application of the switching algebra postulates, laws, and theorems to transform the original expression. 48. What are the disadvantages of algebraic minimisation method? It is hard to recognize when a particular law can be applied and difficult to know if resulting expression is truly minimal. The incorrect implementation or dropped variables etc can easy lead to a mistake. 49. Explain Karnaugh map minimisation? The Karnaugh map provides a systematic method for simplifying a Boolean expression or a truth table function. The K map can produce the simplest SOP or POS expression possible. K-map procedure is actually an application of adjacency and guarantees a minimal expression. It is easy to use, visual, fast and familiarity with Boolean laws is not required. 50. What is a don t care state? When the input combinations are irrelevant or cannot occur, the output states are in the Truth table and the K map are filled with an X and are referred to as don't care states. 51. How to construct a 5 variable K map? A five variable K Map can be constructed using two 4 variable maps side-by-side. The groups spanning both maps occupy the same place in both maps. Module 8: Transistor Transistor Logic 52. What is a TTL? TTL is the short form of Transistor Transistor Logic. As the name suggests they refers to the digital integrated circuits that employ logic gates consisting primarily of bipolar transistors. 53. What is a TTL inverter? The most basic TTL circuit is an inverter. It is a single transistor with its emitter grounded and its collector tied to V CC with a pull-up resistor, and the output is taken from its collector. When the input is high (logic 1), the transistor is driven to saturation and the output voltage i.e. the drop across the collector and emitter is negligible and therefore output voltage is low (logic 0). Page 8 of 12

9 54. What is the main advantage of TTL over DTL? TTL overcomes the main problem associated with DTL (Diode Transistor Logic), i.e., lack of speed. Module 9: CMOS Logic 55. What does the term CMOS refer to? The term 'Complementary Metal-Oxide-Semiconductor' (CMOS), refers to the device technology for fabricating integrated circuits using both n- and p-channel MOSFET's. 56. What are the applications of CMOS? CMOS is the major technology in manufacturing digital IC's and is widely used in microprocessors, memories, and other digital IC's. 57. What are the different Logic Threshold Voltage Levels? 58. What is an Integrated Injection Logic? Integrated Injection Logic eliminates the need for any resistors, capacitors or transistor isolation. This enables an extremely compact logic circuit to be formed which has low power consumption while maintaining the normal speed of transistortransistor logic. I 2 L is built with multiple collector bipolar junction transistors. 59. What are the logic levels of Integrated Injection Logic? High: 0.7V, Low: 0.2V 60. What is the main advantage of Integrated Injection Logic? I 2 L has high noise immunity because it operates by current instead of voltage 61. What is the other name of Integrated Injection Logic? Merged-Transistor Logic Page 9 of 12

10 62. What is Emitter Coupled Logic? Emitter coupled logic (ECL) gates use differential amplifier configurations at the input stage. (ECL) is a non saturated logic, which means that transistors are prevented from going into deep saturation, thus eliminating storage delays. In other words, the transistor is switched on, but not completely on. This is the fastest logic family. 63. What are the operating levels of ECL? ECL circuits operate using a negative 5.2 V supply and the voltage level for high is V and for low is -1.7V 64. What is the major disadvantage of ECL circuit? Biggest problem with ECL is a poor noise margin. Module 10: Memories 65. How are semiconductor memories classified? A distinction is made between read-only (ROM) and read-write (RWM) memories. 66. What are RWM memories? In RWMs contents can be changed in a short time for a virtually unlimited number of times and contents of ROMs are mostly useful for frequent reading and occasional writing. Since RWM memories use active circuitry (transistors) to store the information, they belong to the class of called volatile memories. 67. What are ROM memories? Read-only memories, on the other hand, encode information by the presence or absence of devices. Their data cannot be modified and they belong to the class of nonvolatile memories. 68. What are the different types of Volatile Memories? Static Random Access Memory (SRAM) and Dynamic Random Access Memory (DRAM) are volatile memories. Page 10 of 12

11 69. What is a SRAM? SRAM is used as a cache memory in computers since it offers the fastest write/read (~8ns) speed among all memories. Hardware design of a single SRAM cell consists of 6 transistors. 70. What is a DRAM? A DRAM cell consists of one transistor and one capacitor and it is based on the charge stored in a capacitor. It is superior to SRAM because of its low cost per bit storage; nevertheless it is slower (`50ns). In DRAM, the stored charge in the capacitor can be maintained only for few milli-seconds and therefore, an extra hardware circuit is needed to periodically refresh the data periodically. 71. How Write and Read operations are performed in SRAM? A Write operation is performed by first charging the Bit Line and with values that are desired to be stored in the memory cell. Setting the Word Line high performs the actual write operation, and the new data is latched into the circuit. A Read operation is initiated by pre-charging both Bit Line and to logic 1. Word Line is set high to close NMOS pass transistors to put the contents stored in the cell on the Bit Line and. 72. How Write and Read operations are performed in DRAM? The Read operation begins by precharging the bit line to an intermediate value,v DD /2. The word line is raised to a high potential and the charge stored on capacitor is shared with V DD /2that on the bit line. The change in the bit line voltage is given by the change on the bit line capacitor when the charge stored on capacitor C is shared with the bit line. During the ' Write 1 ' operation, the word line is driven high, the bit line is tied to V DD corresponding to a 1, and voltage across C rises toward V DD - V tn. To ' Write 0' Page 11 of 12

12 in the cell, the bit line is grounded during the write operation and 0V is stored on capacitor C. 73. What are the different non volatile memories? EPROM, EEPROM, FEEPROM 74. What is the disadvantage of diode cell? The disadvantage of a diode cell is that it does not isolate the bit line from the word line. 75. How are Flash Memory Cells categorised? Flash memory cells can be arranged in two popular architectures; the NOR and the NAND architectures. Page 12 of 12

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