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# Introduction

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Sanjeev Patel 4x

Sanjeev Patel 4x

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• 1. Introduction
• 2.
• Digital Computer = H/W + S/W
• Digital implies that the information in the computer is represented by variables that take a limited number of discrete values.
• the decimal digits 0, 1, 2,….,9, provide 10 discrete values, but digital computers function more reliably if only two states are used.
• because of the physical restriction of components, and because human logic tends to be binary(true/false, yes/no),digital component are further constrained to take only two values and are said to be binary.
• 3. Bit = binary digit : 0/1 Program(S/W) A sequence of instruction S/W = Program + Data » The data that are manipulated by the program constitute the data base Application S/W = DB, word processor, Spread Sheet System S/W = OS, Firmware, Compiler, Device Driver
• 4. Digital Components
• Computer Hardware(H/W)
• CPU
• Memory ROM and RAM
• I/O Device Interface: 8251 SIO,
• Input Device: Keyboard, Mouse, Scanner
• Output Device: Printer, Plotter, Display
• Storage Device(I/O): FDD, HDD,
• 5. AND Gate
• 6.
• 7. OR Gate
• 8.
• 9.
• 10.
• 11.
• 12. Boolean Algebra
• Boolean Algebra
• Deals with binary variable (A, B, x, y: T/F or 1/0) +
• logic operation (AND, OR, NOT…)
• Boolean Function: variable + operation
• F(x, y, z) = x + y’z
• George Boole
• Born: 2 Nov 1815 in Lincoln,
• Died: 8 Dec 1864 in Ballintemple,
• County Cork, Ireland
• 13. Boolean Algebra
• Boolean Function: variable + operation
• F(x, y, z) = x + y’z
• Truth Table: Relationship between a function and variable
• 14.
• Purpose of Boolean Algebra
• To facilitate the analysis and design of digital circuit
• Boolean function = Algebraic form = convenient tool
• Truth table (relationship between binary variables ) Algebraic form
• Logic diagram (input-output relationship : ) Algebraic form
• Find simpler circuits for the same function : by using Boolean algebra rules
• 15.
• 16.
• 17.
• 18. De Morgan’s law
• 19.
• 20. Boolean Algebra Rule
• 21. Karnaugh Map
• Karnaugh Map(K-Map)
• Map method for simplifying Boolean expressions
• Minterm / Maxterm
• Minterm : n variables product ( x=1, x’=0)
• Maxterm : n variables sum (x=0, x’=1)
• 2 variables example
• 22. Map
• 23. F = x + y’z
• 24. Adjacent Square Number of square = 2n (2, 4, 8, ….) The squares at the extreme ends of the same horizontal row are to be considered adjacent The same applies to the top and bottom squares of a column The four corner squares of a map must be considered to be adjacent Groups of combined adjacent squares may share one or more squares with one or more group
• 25.
• 26. Half Adder Logic Diagram Truth Table A half adder adds two one-bit binary numbers A and B . It has two outputs, S and C . The simplest half-adder design, pictured on the right, incorporates an XOR gate for S and an AND gate for C . Half adders cannot be used compositely, given their incapacity for a carry-in bit.
• 27. Full Adder A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers, often written as A , B , and C in ; A and B are the operands, and C in is a bit carried in. A full adder can be constructed from two half adders by connecting A and B to the input of one half adder, connecting the sum from that to an input to the second adder, connecting C in to the other input and OR the two carry outputs Logic Diagram Truth Table
• 28. SR Flip-Flop Graphic Symbol Truth Table A SR flip-flop has three inputs, S (for set ), R (for reset ) and C (for clock ). It has an output Q. The undefined condition makes the SR flip-flop difficult to manage and therefore it is seldom used in practice.
• 29. D Flip-Flop Graphic Symbol Truth Table The D flip-flop is a slight modification of the SR flip-flop by inserting an inverter between S and R and assigning the symbol D to the single input. If D=1, the output goes to the state 1, and if D=0, the output of the flip flop goes to the 0 state.
• 30. JK Flip-Flop Graphic Symbol Truth Table Inputs J and K behave like inputs S and R. When inputs J and K are both equal to 1, a clock transition switches the output of the flip-flop to their complement state.
• 31. T Flip-Flop Truth Table Graphic Symbol The T flip-flop is obtained from a JK flip-flop when inputs J and K are connected to provide a single input designated by T. The flip-flop thus has only two conditions.
• 32. Excitation Tables During the design of circuits, we need a table that lists the required input combinations for a given change of state. Such table is called a flip flop excitation table.
• 33. Sequential Circuits
• A sequential circuit is an interconnection of flip-flops and gates.
Example of a Sequential Circuit Ax Bx Ax+Bx A’x x’ A+B (A+B).x A=Ax+Bx, B=A’x y=(A+B).x State Table