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Note for DIGITAL LOGIC DESIGN - DESIGN By UPTU Risers

  • DIGITAL LOGIC DESIGN - DESIGN
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  • uttar pradesh technical university - uptu
  • Computer Science Engineering
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2 Unit I II III IV V Topic Digital System And Binary Numbers: Number System and its arithmetic , Signed binary numbers, Binary codes, Cyclic codes, Hamming Code, the map method up to five variable, Don’t care conditions, POS simplification, NAND and NOR implementation, Quine Mc-Clusky method (Tabularmethod). Combinational Logic: Combinational Circuits: Analysis Procedure, Design procedure, Binary adder -subtractor, Decimal adder, Binary multiplier, Magnitude comparator, Multiplexers, Demultiplexers, Decoders, Encoders. Sequential Logic And Its Applications : Storage elements: latches & flip flops, Characteristic Equations of Flip Flops, Flip Flop Conversion, Shift Registers, Ripple Counters, Synchronous Counters, Other Counters: Johnson & Ring Counter. Synchronous & Asynchronous Sequential Circuits Analysis of clocked sequential circuits with state machine designing, State reduction and assignments, Design procedure. Analysis procedure of Asynchronous sequential circuits, circuit with latches, design procedure, Reduction of state and flow table, Race-free state assignment, Hazards Memory & Programmable Logic Devices: Digital Logic Families: DTL, DCTL, TTL, ECL & CMOS etc., Fan Out, Fan in, Noise Margin; RAM, ROM, PLA, PAL; Circuits of Logic Families, Interfacing of Digital Logic Families, Circuit Implementation using ROM, PLA and PAL; CPLD and FPGA. Digital Logic Design (REC-301) By: Navneet Pal ( Assistant Professor)

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3 UNIT-1 Content            Digital System And Binary Numbers: Number System and its arithmetic Signed binary numbers Binary codes Cyclic codes, Hamming Code The map method up to five variable Don’t care conditions, POS simplification, NAND and NOR implementation, Quine Mc-Clusky method (Tabularmethod). Digital Logic Design (REC-301) By: Navneet Pal ( Assistant Professor)

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4 Very Short Questions and Answers Q1. What are weighed codes? Give examples. Ans: The weighed codes are the codes that have assigned weights or values for each bit position. A code in which each bit position has a certain numeric value assigned. Several such codes exist, such as 8-4-2-1, 7-4-2-1, 6-3-1 -1, Excess – 3 code. Q2. What are cyclic codes? Ans: An (n, k) linear code C is called a cyclic code if any cyclic shift of a codeword is another codeword. That is, Q3. What are self complementing codes? Ans: A self-complementing code is the one in which the members of the number system complement on themselves. This requires the following two conditions to be satisfied. a). The complement of the number should be obtained from that number by replacing 1s with 0s and 0s with 1s. b). The sum of the number and its complement should be equal to decimal 9. Example of a selfcomplementing code is 2-4-2-1 code, Excess-3 code. , BCD code Q4. What are BCD codes? Ans:A special binary code used to directly represent the decimal characters. Each four bit value in BCD represents a single decimal character. Q5. What are alphanumeric codes? Ans: A binary code used to represent the alphabets, numbers and punctuation marks as well as control characters for controlling a printer or display. Eg – ASCII, EBCD Q6. What is an Excess – 3 code? Ans: A self complementing code used to represent BCD numbers. It is self complementing because the 1’s complement is also the 9’s complement of the BCD number. It is widely used in BCD arithmetic circuits. Examble: 1000 of 8421 = 1011 in Excess-3 Q7. What is a Gray code? (or) What is a unit distance code? Give an example Ans:A reflective, unit distance code where only one bit position changes for each adjacent change in value. Q8 What is a reflective code? Ans: A code is said to be reflective when code for 9 is complement for the code for 0, and so is for 8 and 1 codes, 7 and 2, 6 and 3, 5 and 4. Codes 2421, 5211, gray and excess-3 are reflective, whereas the 8421 code is not. Q9. What is meant by parity bit? Digital Logic Design (REC-301) By: Navneet Pal ( Assistant Professor)

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5 Ans: Parity bit is an extra bit included with a binary message to make the number of 1’s either odd or even. The message, including the parity bit is transmitted and then checked at the receiving and for errors. Q.10 Define duality property Ans :Duality property states that every algebraic expression deducible from the postulates of Boolean algebra remains valid if the operators and identity elements are interchanged. If the dual of an algebraic expression is desired, we simply interchange OR and AND operators and replace 1’s by 0’s and 0’s by 1’s. Q11. State De Morgan’s theorem. Ans: De Morgan suggested two theorems that form important part of Boolean algebra. 1) The complement of a product is equal to the sum of the complements. (AB)’ = A’ + B’ 2) The complement of a sum term is equal to the product of the complements. (A + B)’ = A’B’ Q12. What are called don’t care conditions? Ans: In some logic circuits certain input conditions never occur, therefore the corresponding output never appears. In such cases the output level is not defined, it can be either high or low. These output levels are indicated by ‘X’ or‘d’ in the truth tables and are called don’t care conditions or incompletely specified functions Q13. Convert the given expression in canonical SOP form Y = AC + AB + BC Ans: Y = AC + AB + BC =AC(B + B’ ) + AB(C + C’ ) + (A + A’)BC =ABC + ABC’ + AB’C + AB’C’ + ABC + ABC’ + ABC =ABC + ABC’ +AB’C + AB’C’ Q14 Simplify F = ABC +AB’C + A’C + AB’ Ans: F = ABC +AB’C + A’C + AB’ = AC(B+B’) + A’C + AB’ = AC + A’C + AB’ = C + AB’ Q15. Simplify the expression Z= AB + AB’(A’C’)’ Ans: Z= AB + AB’(A’C’)’ = AB + AB’(A+C) = AB + AB’ + AB’C = A (B + B’ +B’C) = A (1+B’C) = A Q16. What are the different classification of binary codes? Ans • Weighted codes • Non - weighted codes • Reflective codes Digital Logic Design (REC-301) By: Navneet Pal ( Assistant Professor)

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