Explains how digital systems such as the computer represent numbers. Covers the basics of boolean algebra and binary math.
Computer architecture
To understand digital signal processing systems, we must
understand a little about how computers compute. The moderndefinition of a
computer is an electronic
device that performs calculations on data, presenting theresults to humans or other computers in a variety of
(hopefully useful) ways.
Organization of a simple computer
Generic computer hardware organization.
The generic computer contains
input devices (keyboard, mouse, A/D (analog-to-digital) converter,
etc.), a
computational unit , and output
devices (monitors, printers, D/A converters). Thecomputational unit is the computer's heart, and usually
consists of a
central processing unit (CPU), a
memory , and an input/output
(I/O) interface. What I/O devices might be present on a givencomputer vary greatly.
A simple computer operates fundamentally in
discrete time. Computers are
clocked devices, in which
computational steps occur periodically according to ticksof a clock. This description belies clock speed: When you
say "I have a 1 GHz computer," you mean that your computertakes 1 nanosecond to perform each step. That is
incredibly fast! A "step" does not, unfortunately,necessarily mean a computation like an addition; computers
break such computations down into several stages, whichmeans that the clock speed need not express the
computational speed. Computational speed is expressed inunits of millions of instructions/second (Mips). Your 1
GHz computer (clock speed) may have a computational speedof 200 Mips.
Computers perform integer (discrete-valued)
computations. Computer calculations can be
numeric (obeying the laws of arithmetic), logical (obeyingthe laws of an algebra), or symbolic (obeying any law you
like).
An example of a symbolic
computation is sorting a list of names. Each computer instruction that performs an elementary
numeric calculation --- an addition, a multiplication, or adivision --- does so only for integers. The sum or product
of two integers is also an integer, but the quotient oftwo integers is likely to not be an integer. How does a
computer deal with numbers that have digits to the rightof the decimal point? This problem is addressed by using
the so-called
floating-point representation of real numbers. At its heart, however,
this representation relies on integer-valued computations.
Representing numbers
Focusing on numbers, all numbers can represented by the
positional notation system .
Alternative number representation systems
exist. For example, we could use stick figure counting orRoman numerals. These were useful in ancient times, but very
limiting when it comes to arithmetic calculations: ever triedto divide two Roman numerals? The
-ary positional
representation system uses the position of digits ranging from0 to
-1 to denote a number.
The quantity
is known as the
base of the number system.
Mathematically, positional systems represent the positiveinteger
as
and we succinctly express
in
base-
as
.
The number 25 in base 10 equals
,
so that the
digits representing this number are
,
, and all other
equal zero. This same number in
binary (base 2) equals 11001(
)and 19 in hexadecimal (base 16). Fractions between zero and
one are represented the same way.
All numbers can be represented by their
sign, integer and fractional parts.
Complex numbers can be thought of as two
real numbers that obey special rules to manipulate them.
Questions & Answers
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
