{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Digital Logic Notes 2

# Digital Logic Notes 2 - Classification of Digital Circuits...

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

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.

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

View Full Document
A binary switch x 1 = x 0 = (a) Two states of a switch S x (b) Symbol for a switch
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

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

View Full Document
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
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

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

View Full Document
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
Inverter Function L(x) = x’ x L 0 1 1 0 S Light Power supply R x

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

View Full Document
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
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

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

View Full Document
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
Analysis of a Logic Circuit f (x 1 ,x 2 ) = x 1 ’ + x 1 • x 2

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

View Full Document
Functionally Equivalent Circuits
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 .

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

View Full Document
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.
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.

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

View Full Document
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
Axioms Complement. (4a) If X = 0, then X’ = 1. (4b) If X = 1, then X’ = 0. Notation. X X' X ~ X ¬

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

View Full Document
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
Precedence By convention, the precedence of operations in a logic expression is the following: Parentheses.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 76

Digital Logic Notes 2 - Classification of Digital Circuits...

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

View Full Document
Ask a homework question - tutors are online