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Convert Octal to Binary

Updated on 19/07/20242,302 Views

Introduction

Octal and binary are the two main number systems expressing numerical value. The binary is a 2-digit number system only using two digits (0 and 1), whereas the octal is an 8-number system with eight distinct digits (0 to 7).

Simple octal-to-binary conversion requires replacing each octal digit with a binary value. Three binary digits are represented by each octal digit. The steps below can be used to translate an octal number to binary:

1. The octal number you wish to convert should be noted down.

2. Replace each octal digit with its equivalent binary value.

3. To create the binary equivalent, combine the resulting binary digits.

In this tutorial, let's learn the various aspects of octal to binary questions, octal to hexadecimal, and also learn to convert octal to binary decimal and hexadecimal and many more!

Overview

To convert an octal number to binary, each octal digit must be replaced with its matching binary representation, which must then be combined to get the binary counterpart. This procedure helps in numerous cases where binary representations are more appropriate and adheres to the core notion of how various number systems can be converted.

How to Convert Octal to Binary?

The easiest way of replacing each octal digit with its binary counterparts results in the conversion. To convert from octal to binary, follow these simple steps:

Step 1: The octal number you wish to convert should be noted down. Take the octal number 354, for instance.

Step 2: Use the conversion table to convert each octal digit into its corresponding binary value:

• 0 (in octal) is 000 (in binary)
• 1 (in octal) is 001 (in binary)
• 2 (in octal) is 010 (in binary)
• 3 (in octal) is 011 (in binary)
• 4 (in octal) is 100 (in binary)
• 5 (in octal) is 101 (in binary)
• 6 (in octal) is 110 (in binary)
• 7 (in octal) is 111 (in binary)

Step 3: Each octal digit should be replaced with its binary equivalent. The conversion for our example (354) would be as follows:

• 3 (in octal) is 011 (in binary)
• 5 (in octal) is 101 (in binary)
• 4 (in octal) is 100 (in binary)

Step 4: To create the final binary representation, combine the binary digits. Bringing together the binary equivalents in Step 3:

Equivalent in binary: 011101100

Therefore, 011101100 is the octal number 354's binary equivalent.

The binary equivalent of the octal number has been successfully created. By repeating the steps above, you may apply the same procedure to any other octal number. Remember that each octal digit translates into three binary digits, and for conversion purposes, you can group the binary digits into sets of three.

Octal to Decimal Conversion

Octal to decimal conversion involves converting a number from the octal number system (base 8) to the decimal number system (base 10). Here's a brief explanation of how it works:

• Octal Number System: In the octal system, numbers are represented using eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit's position represents a power of 8.
• Decimal Number System: In the decimal system, numbers are represented using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. All the positions of the digits represent a power of 10.
• Conversion Process:

Starting from the rightmost digit of the octal number, assign each digit a position value: 8^0, 8^1, 8^2, and so on.

Multiply each octal digit by its corresponding power of 8 and sum up the results.

For example, let's convert the octal number 346 to decimal:

Octal: 3 4 6

Decimal: 3*8^2 + 4*8^1 + 6*8^0 = 216 + 32 + 6 = 254

So, the octal number 346 is equivalent to the decimal number 254.

Remember that when performing conversions, it's essential to keep track of the position values and perform the necessary multiplication and addition steps correctly.

Code:

`#include <stdio.h>int octalToDecimal(int octalNumber) {Â  Â  int decimalNumber = 0, base = 1;Â  Â  while (octalNumber > 0) {Â  Â  Â  Â  int lastDigit = octalNumber % 10;Â  Â  Â  Â  decimalNumber += lastDigit * base;Â  Â  Â  Â  base *= 8;Â  Â  Â  Â  octalNumber /= 10;Â  Â  }Â  Â  return decimalNumber;}int main() {Â  Â  int octalNumber;Â  Â Â Â  Â  printf("Enter an octal number: ");Â  Â  scanf("%d", &octalNumber);Â  Â Â Â  Â  int decimalEquivalent = octalToDecimal(octalNumber);Â  Â  printf("Decimal equivalent: %d\n", decimalEquivalent);Â  Â Â Â  Â  return 0;}`

Decimal to Binary Conversion

Decimal to binary conversion involves converting a number from the decimal number system (base 10) to the binary number system (base 2). Here's a brief explanation of how it works:

• Decimal Number System: In the decimal system, numbers are represented using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. All the positions of the digits represent a power of 10.
• Binary Number System: In the binary system, numbers are represented using two digits: 0 and 1. Each digit's position represents a power of 2.
• Conversion Process:

Starting from the decimal number, repeatedly divide the number by 2 and note the remainders at each step.

The remainders, read in reverse order, give you the binary representation of the decimal number.

For example, let's convert the decimal number 13 to binary:

Decimal: 13

Binary: 1 1 0 1

So, the decimal number 13 is equivalent to the binary number 1101.

In summary, decimal to binary conversion involves dividing the decimal number by 2 and keeping track of the remainders to obtain the binary representation.

Code:

`#include <stdio.h>void decimalToBinary(int num) {Â  Â  if (num == 0) {Â  Â  Â  Â  printf("Binary: 0\n");Â  Â  Â  Â  return;Â  Â  }Â  Â  int binary[32];Â  Â  int index = 0;Â  Â  while (num > 0) {Â  Â  Â  Â  binary[index] = num % 2;Â  Â  Â  Â  num = num / 2;Â  Â  Â  Â  index++;Â  Â  }Â  Â  printf("Binary: ");Â  Â  for (int i = index - 1; i >= 0; i--) {Â  Â  Â  Â  printf("%d", binary[i]);Â  Â  }Â  Â  printf("\n");}int main() {Â  Â  int decimal;Â  Â Â Â  Â  printf("Enter a decimal number: ");Â  Â  scanf("%d", &decimal);Â  Â  decimalToBinary(decimal);Â  Â  return 0;}`

Convert Octal to Binary Using Table

To convert an octal number to binary using a conversion table, follow these steps:

• Create a Conversion Table: Create a table that maps each octal digit to its corresponding binary representation. The octal digits are 0, 1, 2, 3, 4, 5, 6, and 7, and their binary equivalents are 000, 001, 010, 011, 100, 101, 110, and 111 respectively.
• Read the Octal Number: Start from the leftmost digit of the octal number.
• Lookup Binary Equivalents: For each octal digit, look up its binary equivalent from the conversion table.
• Combine Binary Digits: Concatenate the binary equivalents of all the octal digits to get the binary representation of the given octal number.

For example, let's convert the octal number 567 to binary using the conversion table:

 Octal Digit Binary Equivalent 5 101 6 110 7 111

Binary representation of octal 567: 101110111

In short, converting octal to binary using a table involves looking up the binary equivalents of individual octal digits and combining them to obtain the binary representation.

Code:

`#include<stdlib.h>#include <stdio.h>#include<string.h>void octalDigitToBinary(char octalDigit, char *binary) {Â  Â  switch (octalDigit) {Â  Â  Â  Â  case '0':Â  Â  Â  Â  Â  Â  strcat(binary, "000");Â  Â  Â  Â  Â  Â  break;Â  Â  Â  Â  case '1':Â  Â  Â  Â  Â  Â  strcat(binary, "001");Â  Â  Â  Â  Â  Â  break;Â  Â  Â  Â  case '2':Â  Â  Â  Â  Â  Â  strcat(binary, "010");Â  Â  Â  Â  Â  Â  break;Â  Â  Â  Â  case '3':Â  Â  Â  Â  Â  Â  strcat(binary, "011");Â  Â  Â  Â  Â  Â  break;Â  Â  Â  Â  case '4':Â  Â  Â  Â  Â  Â  strcat(binary, "100");Â  Â  Â  Â  Â  Â  break;Â  Â  Â  Â  case '5':Â  Â  Â  Â  Â  Â  strcat(binary, "101");Â  Â  Â  Â  Â  Â  break;Â  Â  Â  Â  case '6':Â  Â  Â  Â  Â  Â  strcat(binary, "110");Â  Â  Â  Â  Â  Â  break;Â  Â  Â  Â  case '7':Â  Â  Â  Â  Â  Â  strcat(binary, "111");Â  Â  Â  Â  Â  Â  break;Â  Â  Â  Â  default:Â  Â  Â  Â  Â  Â  printf("Invalid octal digit: %c\n", octalDigit);Â  Â  }}void octalToBinary(const char *octal, char *binary) {Â  Â  int i = 0;Â  Â  while (octal[i] != '\0') {Â  Â  Â  Â  octalDigitToBinary(octal[i], binary);Â  Â  Â  Â  i++;Â  Â  }}int main() {Â  Â  char octal[100];Â  Â  char binary[400] = ""; Â Â  Â  printf("Enter an octal number: ");Â  Â  scanf("%s", octal);Â  Â  octalToBinary(octal, binary);Â  Â  printf("Binary: %s\n", binary);Â  Â  return 0;}`

Conclusion

The final binary form can be applied to a variety of tasks, including data transfer, digital electronics, and computer programming. In many domains, being able to convert between different number systems is crucial since it makes data representation and manipulation simple. You may deal with numbers in different bases and develop a greater comprehension of how computers and other digital devices receive and store information by mastering the octal to binary conversion.

In conclusion, knowing how to convert an octal number to binary is a fundamental skill that will enable you to work with various number systems and is essential for many different applications in the digital age. You may confidently handle and manage data expressed in octal or binary format with ease if you have a thorough understanding of the conversion procedure.

FAQs

1. How many binary digits are required to represent an octal number?

Each octal digit in an octal number needs to be represented by three binary digits. This is so because binary uses a base-2 number system, whereas octal uses a base-8 system. Each octal digit can have a value between 0 and 7, hence all potential combinations can be represented by three binary digits, which range from 000 to 111.

2. Why is octal used?

Because of its distinct properties, octal is employed in several particular applications. For a few reasons, it is particularly preferred in computer programming and digital electronics:

• Compact representation
• Easy conversion

3. What is the application of the octal number system in daily life?

The octal number system is not frequently utilized in everyday life. It is mostly used in specialized technical disciplines like computer programming and digital electronics, where it can be useful for representing and processing data in small, flexible representations. However, the decimal (base-10) number system is the preferred option in daily life and most calculations.

4. What is the importance of the binary number system?

In computer science, the binary number system is crucial. It provides the framework for how information is represented and processed by computers. All digital information is eventually stored and processed using binary digits (0s and 1s), including text, photos,

videos, and instructions. Binary operations are crucial for data storage, logic processes, and communication inside digital systems due to their simplicity and efficiency.

5. Who invented the octal number system?

Today's version of the octal number system was not created by a single person. It organically developed from prehistoric numeral systems. The octal system first appeared. However, it wasn't until the emergence of computers and digital electronics in the middle of the 20th century that octal was formally formalized and adopted as a conventional number system.

Director of Engineering

Director of Engineering @ upGrad. Motivated to leverage technology to solve problems. Seasoned leader for startups and fast moving orgs. Working â€¦Read More

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