Set_2 - Classification of Digital Circuits Combinational...

Info iconThis preview shows pages 1–20. Sign up to view the full content.

View Full Document Right Arrow Icon
Classification of Digital Circuits Combinational. Output depends only on current input values. Sequential. Output depends on current input values and present state of the circuit, where the present state of the circuit is the current value of the devices’ memory.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
A binary switch x 1 = x 0 = (a) Two states of a switch S x (b) Symbol for a switch
Background image of page 2
Variables and Functions L = 1 the light is on; L = 0 the light is off; The state of the light can be described as a function of the input variable x : L(x) = x S Battery Light x
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
AND Function x1 x2 L 0 0 0 0 1 0 1 0 0 1 1 1 L(x 1 ,x 2 ) = x 1 • x 2 S Power supply S Light x 1 x 2
Background image of page 4
OR Function L(x 1 ,x 2 ) = x 1 + x 2 x1 x2 L 0 0 0 0 1 1 1 0 1 1 1 1 S Power supply S Light x 1 x 2
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example of a Logic Network L(x 1 , x 2 , x 3 ) = ( x 1 + x 2 ) • x 3 S Power supply S Light S X 1 X 2 X 3
Background image of page 6
Inverter Function L(x) = x’ x L 0 1 1 0 S Light Power supply R x
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Logic Gates x 1 x 2 x n x 1 x 2 x n + + + x 1 x 2 x 1 x 2 + x 1 x 2 x n x 1 x 2 x 1 x 2 x 1 x 2 x n (a) AND gates (b) OR gates x x (c) NOT gate
Background image of page 8
Analysis of a Logic Circuit x1 x2 A B f 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Analysis of a Logic Circuit 1 0 1 0 1 0 1 0 1 0 x 1 x 2 A B f Time (c) Timing diagram
Background image of page 10
Analysis of a Logic Circuit f (x 1 ,x 2 ) = x 1 ’ + x 1 • x 2
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Functionally Equivalent Circuits
Background image of page 12
Boolean Algebra 1854, George Boole created a two valued algebraic system which is now called Boolean algebra . 1938, Claude Shannon adapted Boolean algebra to analyze and describe the behavior of circuits built with relays. This adaptation is called switching algebra .
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Switching Algebra In switching algebra the condition of a logic signal is represented by symbolic variables, such as x, y, and/or z, and these variables can only have two values, 0 or 1. Two possible conventions: Positive Logic. Where LOW = 0 and HIGH = 1. Negative Logic. Where LOW = 1 and HIGH =0.
Background image of page 14
Axioms The axioms or postulates of a mathematical system are a minimum set of basic definitions that are assumed to be true, and from which all other information about the system can be derived.
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Axioms Logical multiplication ( , ). (1a) 0 0 = 0 (2a) 1 1 = 1 (3a) 0 1 = 1 0 = 0 Logical addition ( + , ). (1b) 1 + 1 = 1 (2b) 0 + 0 = 0 (3b) 1 + 0 = 0 + 1 = 1
Background image of page 16
Axioms Complement. (4a) If X = 0, then X’ = 1. (4b) If X = 1, then X’ = 0. Notation. X X' X ~ X ¬
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Axioms The axioms stated below embody the “digital abstraction” by formally stating that X can take on only one of two values. X = 0 if X 1 X = 1 if X 0
Background image of page 18
By convention, the precedence of operations in a logic expression is the following: Parentheses. Complement.
Background image of page 19

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 20
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 76

Set_2 - Classification of Digital Circuits Combinational...

This preview shows document pages 1 - 20. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online