Immerse yourself in the captivating universe of number systems, where we will explore various methods of representing numbers. Our journey commences with the familiar decimal number system, where we count in multiples of ten. Subsequently, we will venture into the binary system, where counting is accomplished solely using zeros and ones, and the hexadecimal system, where we employ sixteen distinct symbols. Let us not overlook the octal system, which utilizes eight symbols! Throughout this expedition, you will acquire the skills to convert between these systems, unlocking the secrets of numerical representation. Whether you possess an aptitude for mathematics or simply possess a curious mind, this odyssey will expand your understanding of numbers and their diverse systems. Prepare yourself to decipher the language of numbers!
Number system can be converted to another number system ,the number system can be converted into following ways
In the previous blog we have discussed the following topics
Binary To Decimal
Decimal to Binary
Octal to Decimal
Decimal To Octal
Hexadecimal to Decimal
Decimal to Hexadecimal
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In this blog we are discussing the Following Topics
Binary to Octal & Vice Versa
Binary to Hexadecimal & Vice Versa
Octal to Hexadecimal & Vice versa
Number System Conversion
Binary to Octal Conversion
To convert a binary number to octal, we should follow the following steps
Step 1 we can group the binary digits into groups of 3, starting from the rightmost digit.
Step 2 Each group of 3 binary digits corresponds to a single octal digit.
Step 3 Then we convert each group to its octal equivalent.
Step 4 We then concatenate them together to get the octal equivalent
Step 5 If the last group of binary digits is than 3, so we need to add leading zeros to complete the group.
Example
Step 1To convert the binary number 11011011010 to octal,
Step 2 we group the binary digits into groups of 3, starting from the rightmost digit: 011 011 011 010.
Step 3 Then we convert each group to its octal equivalent. 011 corresponds to 3, 011 corresponds to 3, 011 corresponds to 3, 010 corresponds to 2.
Step 4 We then concatenate them together to get the octal equivalent of 11011011010, which is 3332.
Binary to Octal Conversion
Octal to Binary Conversion
To convert an octal number to binary, we should follow the following steps
Step 1 we can first convert each octal digit to its binary equivalent
Step 2 Then concatenate them together.
Step 3 Each octal digit corresponds to 3 binary digits. if the conversion is less the three digits then add 0 to the leftmost digit
For example, to convert the octal number 512 to binary
Step 1 we first convert the digit 5 to its binary equivalent, which is 101,
Step 2 Then convert the digit 1 to its binary equivalent, which is 001.
Step 3 Then convert the digit 2 to its binary equivalent, which is 010.
Step 4 We then concatenate them together to get the binary equivalent of 512, which is 101001010.
Octal to Binary Conversion
Binary to Hexadecimal Conversion
To convert a binary number to hexadecimal, we should follow the following steps
Step 1 we can group the binary digits into groups of 4, starting from the rightmost digit.
Step 2 Each group of 4 binary digits corresponds to a single hexadecimal digit.
Step 3 Then we convert each group to its hexadecimal equivalent.
Step 4 We then concatenate them together to get the hexadecimal equivalent
Step 5 If the last group of binary digits is less than 4, so we need to add leading zeros to complete the group.
Example,
Step 1 convert the binary number 110 1101 1010 to hexadecimal,
Step 2 we group the binary digits into groups of 4, starting from the rightmost digit: 110 1101 1010
Step 3 Add Leading zero to complete the group
Step 4 0110 1101 1010
Step 3 convert each group to its hexadecimal equivalent. Like 0110 to 6, 1101 corresponds to D, 1010 corresponds to A.
Step 4 We then concatenate them together to get the hexadecimal equivalent of 11011011010, which is 6DA.
Binary to Hexadecimal Conversion
Hexadecimal to Binary Conversion
To convert a hexadecimal number to binary, we should follow the following steps
Step 1 we can first convert each hexadecimal digit to its binary equivalent
Step 2 Then concatenate them together.
Step 3 Each hexadecimal digit corresponds to 4 binary digits.
Step 4 If any hexadecimal digit has less than 4 binary digit , so we need to add leading zeros to complete the group.
For example,
To convert the hexadecimal number A6 to binary,
Step 1 we first convert the digit A to its binary equivalent, which is 1010,
Step 2 Then convert the digit 6 to its binary equivalent, which is 110. as it has only 3 digits so we add leading 0 to complete the group.
Step 3 Then we concatenate them together to get the binary equivalent of A5, which is 10100110.
Hexadecimal to Binary Conversion
Hexadecimal to Octal Conversion:
To convert a hexadecimal number to octal, we should follow the following steps
step 1 We first convert the hexadecimal to binary
Step 2 Then group the binary digits into groups of 3, starting from the rightmost digit.
Step 3 Each group of 3 binary digits corresponds to a single octal digit.
Step 4 Then we convert each group to its octal equivalent.
Step 5 We then concatenate them together to get the octal equivalent
For example,
To convert the hexadecimal number A6 to octal,
Step 1 we first convert A6 to binary which is 1010 0110 by Hexadecimal to binary conversion method
Step 2 Then group the binary digits into groups of 3: 010 100 110.
Step 3 Then we convert each group to its octal equivalent. 010 corresponds to 2, 100 corresponds to 4, 110 corresponds to 6.
Step 4 We then concatenate them together to get the octal equivalent of A6, which is 246.
Hexadecimal to Octal Conversion
Octal to Hexadecimal Conversion:
To convert an octal number to hexadecimal, we should follow the following steps
Step 1 we first convert the Each octal number to binary number
Step 2 Then group the binary digits and divide into groups of 4,
Step 3 Starting from the rightmost digit.
Step 4 Each group of 4 binary digits corresponds to a single hexadecimal digit. convert each group into hexadecimal number
For example,
To convert the octal number 512 to hexadecimal,
Step 1 we first convert 512 to binary which is 101 001 010
Step 2 Then group the binary digits 101001010
Step 3 Divide into groups of 4: 0001 0100 1010.
Step 4 Then we convert each group to its hexadecimal equivalent.
0001 corresponds to 1,
0100 corresponds to 4,
1010 corresponds to 10.
Step 5 We then concatenate them together to get the hexadecimal equivalent of 1 4 10, which is 14A.
Octal to Hexadecimal Conversion
Frequently Asked Question(FAQ)
How to convert Binary no to Octal no ?
To convert a binary number to a octal number, follow these steps:
Step 1 we can group the binary digits into groups of 3, starting from the rightmost digit.
Step 2 Each group of 3 binary digits corresponds to a single octal digit.
Step 3 Then we convert each group to its octal equivalent.
Step 4 We then concatenate them together to get the octal equivalent
Step 5 If the last group of binary digits is than 3, so we need to add leading zeros to complete the group.
How to convert Octal no to Binary no?
Step 1 we can first convert each octal digit to its binary equivalent
Step 2 Then concatenate them together.
Step 3 Each octal digit corresponds to 3 binary digits. if the conversion is less the three digits then add 0 to the leftmost digit
How to convert Binary no to Hexadecimal no ?
Step 1 we can group the binary digits into groups of 4, starting from the rightmost digit.
Step 2 Each group of 4 binary digits corresponds to a single hexadecimal digit.
Step 3 Then we convert each group to its hexadecimal equivalent.
Step 4 We then concatenate them together to get the hexadecimal equivalent
Step 5 If the last group of binary digits is less than 4, so we need to add leading zeros to complete the group.
How to convert HexaDecimal number to Binary number ?
Step 1 we can first convert each hexadecimal digit to its binary equivalent
Step 2 Then concatenate them together.
Step 3 Each hexadecimal digit corresponds to 4 binary digits.
Step 4 If any hexadecimal digit has less than 4 binary digit , so we need to add leading zeros to complete the group.
How to convert Hexadecimal number to octal number ?
step 1 We first convert the hexadecimal to binary
Step 2 Then group the binary digits into groups of 3, starting from the rightmost digit.
Step 3 Each group of 3 binary digits corresponds to a single octal digit.
Step 4 Then we convert each group to its octal equivalent.
Step 5 We then concatenate them together to get the octal equivalent
How to convert Octal number to Hexadecimal number ?
Step 1 we first convert the Each octal number to binary number
Step 2 Then group the binary digits and divide into groups of 4,
Step 3 Starting from the rightmost digit.
Step 4 Each group of 4 binary digits corresponds to a single hexadecimal digit. convert each group into hexadecimal number
Conclusion
In conclusion , this blog cover the number and their conversion method ,In summary, i can say that how crucial number systems are, they play an important role in both technology and mathematics. Proficiency in comprehending the various types of number systems and their conversions can prove beneficial in diverse domains like computer science and electrical engineering.
in this Blog i covered the following number system conversion ,
Binary to Octal & Vice Versa
Binary to Hexadecimal & Vice Versa
Octal to Hexadecimal & Vice versa
I hope this blog helps you a lot Happy learning....
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