B sc cs i bo-de u-iii combitional logic circuit
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This document provides an overview of digital electronics, focusing on logic circuits and combinational logic circuits. It discusses the basics of combinational logic, including standard combinational circuits like adders, subtractors, and multiplexers. It also covers the analysis and design of combinational logic, including examples like a magnitude comparator. Finally, it discusses common combinational logic components like decoders, multiplexers, and full adders.
B sc cs i bo-de u-iii combitional logic circuit
- 1. Basics of Digital Electronics Course: B.Sc.(CS) Sem.:1st
- 2. LOGIC CIRCUITS: 1) Combinational 2) Sequential Combinational logic circuits (circuits without a memory): Combinational switching networks whose outputs depend only on the current inputs. Sequential logic circuits (circuits with memory): In this kind of network, the outputs depend on the current inputs and the previous inputs. These networks employ storage elements and logic gates.
- 3. COMBINATIONAL CIRCUITS Most important standard combinational circuits are: • Adders • Subtractors • Comparators • Decoders • Encoders • Multiplexers Available in IC’s as MSI and used as standard cells in complex VLSI (ASIC)
- 7. DESIGN OF COMBINATIONAL LOGIC 1. From the specifications of the circuit, determine the number of inputs and outputs 2. Derive the truth table that defines the relationship between the input and the output. 3. Obtain the simplified Boolean function using x- variable K-Map. 4. Draw the logic diagram and verify the correctness of the design.
- 8. DESIGN OF COMBINATIONAL LOGIC Example: Design a combinational circuit with three inputs and one output. The output is a 1 when the binary value is less than three. The output is 0 otherwise.
- 9. BINARY ADDER – Half Adder Implementation of Half Adder
- 10. BINARY ADDER - Full Adder
- 11. Full Adder in SOP
- 12. Implementation Full Adder with two half Adders
- 13. 4-BIT FULL ADDER 4 bit Adder
- 14. Magnitude Comparator A magnitude comparator is a combinational circuit that compares two numbers, A and B, and then determines their relative magnitudes. A > B A = B A < B Algorithm Consider two numbers, A and B, with four digits each: A=A3 A2 A1 A0 B=B3 B2 B1 B0 xi=1 if A=B=0 or A=B=1 xi=AiBi+ Ai’Bi’ for i=0,1,2,3 XNOR For equality to exist, all xi variables must be equal to 1: (A=B)=X3 X2 X1 X0 AND Operation
- 15. Magnitude Comparator To determine if A is greater than or less than B, we inspect the relative magnitudes of significant digits. If the two digits are equal, we compare the next lower significant pair of digits. The comparison continues until a pair of unequal digits is reached. The sequential comparison can be expressed by:
- 16. DECODERS A decoder is a combinational circuit that converts binary information from n input lines to an 2nunique output lines. Some Applications: a) Microprocessor memory system: selecting different banks of memory. b) Microprocessor I/O: Selecting different devices. c) Memory: Decoding memory addresses (e.g. in ROM). d) Decoding the binary input to activate the LED segments so that the decimal number can be displayed.
- 17. 3-to-8-line DECODER If the input corresponds to minterm mi then the decoder ouput i will be the single asserted output.
- 19. 2-to-4-line DECODER with Enable The decoder is enabled when E = 0. The output whose value = 0 represents the minterm is selected by inputs A and B. The decoder is inactive when E=1 D0………D3 =1 A Decoder with enable input is called a decoder/demultiplexer. Demultiplexer receives information from a single line and directs it to the output lines.
- 20. A 4 x 16 DECODER When w = 0, the top decoder is enabled and the bottom is disabled. Top decoder generates 8 minterms 0000 to 0111, while the bottom decoder outputs are 0’s. When w = 1, the top decoder is disabled and the bottom is enabled. Bottom decoder generates 8 minterms 1000 to 1111, while the top decoder outputs are 0’s.
- 22. MULTIPLEXERS/DATA SELECTORS A multiplexer is a combinational circuit that selects one of many input lines (2n ) and steers it to its single output line. There are (2n ) and n selection lines whose bit combinations determine which input is selected.
- 23. 4-to-1LINE MULTIPLEXER DESIGN In general, a 2n –to–1- line multiplexer is constructed from an n–to 2n decoder by adding to 2n it lines, one to each AND gate.
- 24. References Digital Logic and Computer Design – M. Morris Mano – Pearson Fundamentals of Digital Circuits – A. Anand Kumar - PHI Digital Electronics - Gothmen - PHI Digital Electronics Principles - Malvino & Leech - MGH Digital Electronics -Tokneinh - MGH
- 25. Web References www.engrcs.com/courses/engr250/engr250lecture.pdf www.eng.auburn.edu/~strouce/class/elec4200/design en.wikipedia.org/wiki/Combinational_logic www.allaboutcircuits.com › ... › Combinational Logic Functions www.cs.umd.edu/class/sum2003/cmsc311/Notes/Comb /gates.htm