Computer systems rely heavily on numbering systems to perform calculations. At the heart of these systems are four major notations, called the decimal, binary, octal, and hexadecimal systems.

The type of numbering system used depends on the application, and understanding how to convert from one system to another is a crucial skill. In this article, we will examine two topics.

First, we will delve into the conversion of hexadecimal numbers to decimal numbers, exploring different methods for taking a hexadecimal value and converting it to its decimal equivalent. Second, we will take an in-depth look at the most popular numbering systems in computer science, including the decimal system, binary system, octal system, and hexadecimal system.

## Conversion of Hexadecimal Number to Decimal Number

The hexadecimal system, also known as the base-16 numbering system, is commonly used in computer systems. It uses a set of symbols from 0 to 9 and A to F character to represent values.

However, sometimes it becomes necessary to convert a hexadecimal value to its decimal equivalent. Method 1: Using Obase, Ibase, and Bc

The first method involves using the shell command-line tool to convert the hexadecimal number to a decimal value.

This method requires the use of the obase, ibase, and bc commands. Essentially, these tools convert the input-base to output-base and perform the calculation.

Method 2: Using Ibase, Command-Line Argument, and Bc

This method involves using the command-line argument to specify the input-base and the bc command to perform the conversion. The key difference is that we dont need to change the output-base; it is already set as

10 by default.

Method 3: Using Printf Method

The scanf and printf functions in C programming language are very handy in converting data from one form to another. This method involves using printf() function to convert hexadecimal to decimal value.

Method 4:

## Using Double Brackets

The double brackets method is similar to the first method, but it involves parentheses that specify a base in the expression. These brackets are used to represent an arithmetic expression in a specific base.

## Method

5: Converting a List of Hexadecimal Numbers

Sometimes, you may want to convert a list of hexadecimal numbers in a text file. This can be done using a while loop.

The while loop reads one hexadecimal number at a time, converts it to decimal using the previous methods, and prints the result until the end of the file is reached.

## Popular Number Systems in Computer Systems

## Decimal System

The decimal system, or base-

10 numbering system, is the most familiar to most people. It consists of ten digits, ranging from 0 to 9.

In this system, each digit position has a value ten times that of the position to its right. For example, the number 1234 in the decimal system can be written as:

1*

10^3 + 2*

10^2 + 3*

10^1 + 4*

10^0=

1000+200+30+4 = 1234

## Binary System

The binary system, or base-2 numbering system, has only two digits: 0 and 1. In this system, each digit represents the value 2 raised to a power of a position.

For example, the binary number

## 1011 can be written as:

1*2^3 + 0*2^2 + 1*2^1 + 1*2^0=8+0+2+1=11

## Octal Number System

The octal system, or base-8 numbering system, uses eight digits from 0 to 7. In this system, each digit position has a value eight times that of the position to its right.

For example, the octal number 372 can be written as:

3*8^2 + 7*8^1 + 2*8^0=192+

56+2=2

## 50

## Hexadecimal Number System

The hexadecimal system, or base-16 numbering system, uses a set of 16 digits that start from 0 to 9 and then A to F characters. In this system, each digit represents the value 16 raised to a power of a position.

For example, the hexadecimal number 1A

## 5 can be written as:

1*16^2 +

10*16^1 +

5*16^0=2

56+160+

5=421

## Conclusion

Conversion of numbering systems is an essential skill in the world of computer systems. Knowing how to convert numbers between different systems can make data processing and storage more efficient.

Understanding the four most significant numbering systems in computer science, including the decimal, binary, octal, and hexadecimal systems, is crucial in developing software solutions. Thanks for reading and make sure to practice the methods discussed here, which will improve your ability to convert, manipulate, and store data in different numbering formats.

## Methods for Converting Number Systems in Bash

In computer programming, numbers are represented in different systems such as decimal, binary, octal, and hexadecimal. As a developer, it’s essential to be able to convert between these numbering systems.

In this article, we will explore the different methods available in bash to convert numbers between various numbering systems. Using obase, ibase and bc

One method for converting between numbering systems in bash is using the “obase” and “ibase” variables and the “bc” command.

“ibase” specifies the input numbering system, while “obase” specifies the output numbering system. “bc” stands for basic calculator and performs the conversion.

Here’s an example that shows how to convert a binary number (

## 10

10) to decimal using this method:

“`

echo “ibase=2; obase=

10;

## 10

10″ | bc

“`

## The output will be the decimal equivalent of

## 10

## 10 in binary:

“`

## 10

“`

## Using Command Line Argument and bc

A different method of using the “bc” command to convert numbers is by using command-line arguments. In this approach, the number to be converted and the input numbering system are passed as command-line arguments.

The output will be the decimal equivalent of the original number. Here’s an example that shows how to convert a hexadecimal number to decimal:

“`

echo “obase=

10; ibase=16; $HEX” | bc

“`

Here, $HEX is a shell variable that holds the hexadecimal number to be converted.

The “ibase” variable specifies that the input is in hexadecimal, and the “obase” variable specifies that the output should be decimal.

## Using printf Method

The printf command can be used to output numbers in different numbering systems. It uses a format string to specify the output format.

The “printf” command in bash has a “%x” option that prints numbers in hexadecimal format. Similarly, we can use “%o” to print numbers in octal format and “%d” for decimal format.

Here’s an example that shows how to convert a decimal number to hexadecimal:

“`

printf “%xn” 1234

“`

## The output will be the hexadecimal value of 1234:

“`

## 4d2

“`

## Using Double Brackets

The double brackets method is another way to convert numbers between different numbering systems in bash. It involves enclosing the number to be converted in double brackets and specifying the input numbering system using a prefix.

The output numbering system is specified by an arithmetic expression that is evaluated using the double brackets construct. Here’s an example that shows how to convert a binary number to decimal using double brackets:

“`

echo $((2#

## 101))

“`

The output will be the decimal equivalent of binary number “

101″:

“`

## 5

“`

## Converting a List of Numbers

Sometimes, you may need to convert a list of numbers in a text file from one numbering system to another. In this case, you can use a while loop to iterate over the file, read each line, and convert the number using one of the methods discussed above.

Here’s an example that shows how to convert all numbers in a file from hexadecimal to decimal:

“`

## while read -r line

## do

printf “%dn” “0x${line}”

done < file.txt

“`

The “read” command reads a line from the file, and the “printf” command converts the line from hexadecimal to decimal using the “%d” format specifier. The “0x” prefix specifies that the input is in hexadecimal.

## Conclusion

Converting between numbering systems is an essential skill for developers, and there are various ways to do this in bash. This article covered five different methods that can be used to convert numbers in bash.

Whether you need to convert a single number or a list of numbers, these methods will come in handy. Converting numbers between different numbering systems is an essential skill for developers, and bash provides several methods to achieve this.

This article explored five different methods for converting numbers in bash, including using “obase,” “ibase,” “bc,” command-line arguments, printf method, double brackets, and a while loop. Each method has its advantages and disadvantages, depending on the specific use case.

Being able to convert numbers between different numbering systems is crucial in developing software solutions that process data efficiently. As a developer, familiarizing yourself with these methods and selecting the most appropriate technique for a specific problem is crucial.