ece 2010 exam 1

Analog Signal

a continuous signal which can take on an infinite number of values over a range.

Digital Signal

a discrete signal which can only have a finite number of values over a given range, and only a finite number of samples over a given time period

Arabic Number System

This is the system we use today. Invented by the Indians and the Muslims. Much easier to use than the Roman Number System. This was significant because more people could understand numbers/math/science, which lead to more inventions and more mathematical and scientific advances.

ternary number system

number system based off a base of 3

binary number system

number system with a base of 2. only 2 symbols 1's and 0's which are called bits

2^0

1

2^3

8

2^4

16

2^5

32

2^6

64

2^7

128

2^8

256

2^9

512

2^10

1024

1 GB

2^30 bytes

1 K

2^10 bytes

NRZ-L (Non return to Zero Level)

Transmit 1s as zero voltage and 0s as positive voltage

NRZ-I

1's and 0's are represented by an inversion(switching) of the signal. If the signal transitions, it is a 1, else a 0.

Return-to-Zero (RZ) Polar

Essentially the same as NRZ-L, but during the bit interval, the signal changes back to zero to allow for synchronization

Bi-phase

The data values are based on the transitions of the signal instead of the levels.

Manchester Bi-phase

A positive transition at the middle of a bit period represents a 1, and a negative transition is a 0.

Amplitude Shift Keying (ASK)

A 0 is represented by a different amplitude than that of a 1

Frequency Shift Keying (FSK)

A 0 is represented by a different frequency than that of a 1.

Phase Shift Keying (PSK)

A 0 is represented by a different phase shift than that of a 1.

Quadrature Amplitude Modulation (QAM)

Combines both amplitude and phase modulation to produce eight different values (000 to 111).

what operator is this truth table for

and (*)

what operator is this truth table for

or(+)

what operator is this truth table for

not(‘)

what is this

and

what is this

or

what is this

not

Closure

A set S is “closed” with respect to a binary operator if for every pair of elements of S, the operator specifies a rule for obtaining a unique element of S.

Associative Law

A binary operator * on a set S is said to be “associative” whenever

Commutative Law

A binary operator * on a set S is said to be “commutative” whenever

Identity Element

A set S is said to have an “identity element” with respect to a binary operator * on S if there exists an element e of S with the property that

Inverse Elements

A set S with an identity element e with respect to the binary operator * is said to have an “inverse element” whenever, for every x of S, there exists an element y of S such that x * y = e

Distributive Law

Group

an example of an algebraic structure consisting of a set and binary operation which satisfies the properties of closure and associativity, and also has an identity element and every element has an inverse element

field

lgebraic structure which is a commutative group that contains a second operation that also has inverses and provides distributivity with the first operation

ring

a like a field, but the second operator does not necessarily have an inverse element

Postulate 1

(a) The structure is closed with respect to the + operator.

(b) The structure is closed with respect to the x operator.

Postulate 2

(a) The element 0 is an identity element with respect to +.

(b) The element 1 is an identity element with respect to x.

Postulate 3

(a) The structure is commutative with respect to +.

(b) The structure is commutative with respect to x

Postulate 4

(a) The operator x is distributive over +.

(b) The operator + is distributive over x.

Postulate 5

Postulate 6

Postulate 2 (Identity)

Postulate 5 (Complementation)

Theorem 1 (Idempotence)

Theorem 2 (Annihilation)

Theorem 3 (Involution)

Postulate 3 (Commutative)

Theorem 4 (Associative)

Postulate 4 (Distributive)

Theorem 5 (DeMorgan)

Theorem 6 (Absorption)

Join Property

Cancellation of OR” Property

consensus theorem

order of operations

1. Parentheses

2. NOT

3. AND

4. OR

The “FOIL Method”

Literal

each mention of a variable ex (X,Y’,Z’)

Term

each product (XY’ , XYZ’ , Y"‘Z)