Why is it necessary to convert a binary number into an octal number?
Table of Contents
- 1 Why is it necessary to convert a binary number into an octal number?
- 2 When converting binary digits to its octal equivalent We use this grouping method?
- 3 What is the binary equivalent of the octal number 3?
- 4 What is the proper way of converting octal numbers to decimal values?
- 5 Why is octal 3 bit?
- 6 How do you convert to binary?
- 7 How do we convert binary to decimal?
- 8 What is the relationship between binary and octal?
Why is it necessary to convert a binary number into an octal number?
Conversion from Binary to Octal number system Octal number system provides convenient way of converting large binary numbers into more compact and smaller groups.
When converting binary digits to its octal equivalent We use this grouping method?
Conversion from Binary to Octal
- Take the given binary number.
- Multiply each digit by 2n-1 where n is the position of the digit from the decimal.
- The resultant is the equivalent decimal number for the given binary number.
- Divide the decimal number by 8.
- Note the remainder.
How many bits in a binary number are grouped together to get octal number?
3 bits
We use only 3 bits to represent Octal Numbers. Each group will have a distinct value between 000 and 111. Note: Octal number system supports only digits from 0 to 7. Beyond 7, such as 8 and 9 are not octal digits.
What is the binary equivalent of the octal number 3?
Conversion from Octal to Binary number system
| Octal Symbol | Binary equivalent |
|---|---|
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
What is the proper way of converting octal numbers to decimal values?
Step 1) Write down the place value of each digit. Step 2) Add up the place value of each digit. So 275 in octal is equal to 189. 2) Convert 3250 from octal into decimal.
What should be added to last group of 3 bits if the MSB side does not have 3 bits while converting numbers from binary to octal?
Zeros must be added to the left of the MSB to produce even groups of 3 bits when converting from binary to octal.
Why is octal 3 bit?
The main advantage of using Octal numbers is that it uses less digits than decimal and Hexadecimal number system. So, it has fewer computations and less computational errors. It uses only 3 bits to represent any digit in binary and easy to convert from octal to binary and vice-versa.
How do you convert to binary?
How to convert decimal to binary
- Divide the number by 2.
- Get the integer quotient for the next iteration.
- Get the remainder for the binary digit.
- Repeat the steps until the quotient is equal to 0.
What is the rule for decimal to binary?
The rules to convert decimal to binary numbers are given below:
- Write down the number.
- Divide it by 2 and note the remainder.
- Divide the quotient obtained by 2 and note the remainder.
- Repeat the same process till we get 0 as the quotient.
- Write the values of all the remainders starting from the bottom to the top.
How do we convert binary to decimal?
To convert a number from binary to decimal using the positional notation method, we multiply each digit of the binary number with its base, (which is 2), raised to the power based on its position in the binary number.
What is the relationship between binary and octal?
We can see the 3 to 1 relationship between octal and binary when we compare their bases. Octal has a base of 8 or 23 and binary has a base of 2 or 21. As you might guess, binary and hexadecimal have a 4 to 1 relationship since the base of hexadecimal is 16 or 24.