number systems The study of digital systems is very important from the perspective of understanding how data is represented before any digital system including digital computers is processed.
In this chapter, we will discuss the different number systems that are commonly used to represent data. We will start the discussion with the decimal number system.
Although this is not important from a digital electronics point of view, it will be briefly outlined to explain some basic concepts used in other digital systems.
Then there are the more commonly used number systems, such as binary, octal, and hexadecimal number systems.
what are number systems
There are two basic methods to represent the numerical values of various physical quantities that we constantly deal with in our daily lives.
One method called simulation is to represent the numerical value of the quantity as a continuous range of values between two expected extreme values.
For example, depending on the accuracy of the measuring instrument, the temperature of the oven can be set from 0 to 100°C, and it can be measured as 65°C or 64.96°C or 64.958°C or even 64.9579°C. Similarly, the voltage across a component in an electronic circuit can be measured as 6.5 V or 6.49 V or 6.487 V or 6.4869V.
The basic concept of this way of expression is that the change of the numerical value is continuous and can have any theoretically possible infinite value between the two extremes.
Another possible way, called a number, represents a numerical value represented by a discrete value step by step.
Numerical values are mostly expressed in binary numbers. For example, the temperature of the oven can be expressed as 64°C, 65°C, 66°C, etc. in 1°C steps.
In summary, when the analog representation provides a continuous output, the digital representation produces a discrete output.
An analog system includes equipment that processes or processes various physical quantities represented in analog form.
Digital systems include devices that process physical quantities represented in digital form.
The advantages of digital technology and systems are that they are relatively easy to design, and have higher accuracy, programmability, noise resistance, easier to store data, and easy to manufacture in the form of integrated circuits, which leads to the use of smaller size and more complex functions.
However, the real world is simulated. Essentially, most physical quantities (such as position, velocity, acceleration, force, pressure, temperature, and flow rate) are analog quantities.
This is why if we want to benefit from the functions and convenience brought by the use of digital technology, then the analog variables representing these quantities need to be digitized or discretized in the input.
In a typical system that handles analog input and output, the analog is digitized at the input with the help of an analog-to-digital converter module and then converted back to analog form at the output using a digital-to-analog converter module.
The second half of this book discusses analog-to-digital converters and digital-to-analog converter circuits in detail.
the number systems
We will start discussing various digital systems by briefly describing the parameters common to all digital systems. An understanding of these parameters and their relevance to digital systems is essential to understanding how various systems work.
base number systems
The different characteristics that define a number system include the number of independent numbers used in the number system, the position value of the different numbers that make up the number, and the largest number that can be written with a given number of digits. It is called the base or base of the number system.
The decimal system that we are all familiar with can be said to have a base of 10 because it has 10 independent numbers, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Similarly, a binary with only two independent digits 0 and 1 is a base-2 number system. The bases (or bases) of octal and hexadecimal numbers are 8 and 16, respectively.
In the following sections, we will see that the base of the number system also determines two other characteristics.
The position value of the different numbers in the integer part of the number is given by r0, r1, r2, r3, etc., starting from the number adjacent to the decimal point.
For the decimal part, they are r-1, r-2, r-3, etc., and start with the number next to the decimal point.
Here, r is the base of the. Likewise, the largest number that can be written with n digits in a given number system is equal to rn.
Types of number systems
number system questions
Decimal Number System
Binary Number System
Octal Number System
Hexadecimal Number System
The number system (or number system) is a writing system used to express numbers. That is, a mathematical symbol used to use numbers or other symbols to represent numbers in a given set in a consistent manner. The same sequence of symbols can represent different numbers in different number systems.
There are several systems for representing the counting numbers. … The usual “base ten” or “decimal” system: 1, 2, 3, … , 10, 11, 12, … 99, 100, …. Roman numerals
As a result, the decimal binary has been described as the best number system. In its factors, 2 and 3 are prime numbers, representing the reciprocal of all 3 smooth numbers (for example, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, … ) Termination representation in decimal binary representation.
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