Octal number conversion like Octal to Decimal Converter, Octal to Binary Converter, and Octal to Hexadecimal Converter.
Note
MSB
MSB (Most Significant Bit) is the leftmost digit is the most significant digit of a number.
LSB
LSB (Least Significant Bit) is the rightmost digit is the least significant digit of a number.
Octal to Decimal Converter
What is Octal Number? The number to the base 8 is called octal numbers. It uses the numbers from 0 to 7. What is Decimal Number? Decimal number system has basic digits 0 to 9. The base of the decimal system is 10.
For Example
To convert the Octal number (65)8to a Decimal number ( )10, we use the Multiplication method.
| Steps | Description | Solution |
|---|---|---|
| 1 | Write down the octal number | (65)8 |
| 2 | Count right to left of the octal number. | 1 0 6 5 |
| 3 | List the powers of eight from right to left. Start at 80, evaluating it as “1”. Increment the exponent by one for each power. |
1 0 6 5 81 80 |
| 4 | Multiply each digit of the Octal number by the corresponding power of 8 | 6×81 + 5×80 |
| 5 | Add all the numbers to get the decimal equivalent. | = 6×81 + 5×80 = 6×8 + 5×1 = 48 + 5 = 53 (65)8 = (53)10 |
Octal to Binary Converter
What is Binary Number? Binary number contained only two digits or bits; 0and 1. Therefore, base of the system is 2. There are mainly two ways to convert octal number to binary number.
Indirect Method
In indirect method first we need to convert octal number to decimal number then we can convert that decimal number to binary number.
For Example
Convert Octal number (65)8to Binary number ( )2
A) First, we convert Octal number (65)8to Decimal number ( )10, we use the Multiplication method. Octal to Decimal Converter
B) Secondly, we convert Decimal number ( )10 to Binary number ( )2, we use the Division method.
| Steps | Description | Solution |
|---|---|---|
| 1 | Divide decimal number by 2 until quotient is 0. | 53/2 = 26 Remainder is 1 26/2 = 13 Remainder is 0 13/2 = 6 Remainder is 1 6/2 = 3 Remainder is 0 3/2 = 1 Remainder is 1 1/2 = 0 Remainder is 1 |
| 2 | The last remainder obtained from the division is the most significant bit (MSB) of the binary number. Hence arrange the number from the most significant bit (MSB) to the least significant bit (LSB). Read from the bottom (MSB) to top (LSB). | (53)10 = (110101)2 |
Octal number (65)8to Binary number (110101)2
Direct Method
In this method, we grouped octal number and replace their equivalent binary number. To get binary number of given octal number, we have to convert octal number into its 3 bit binary equivalent.
For Example
Convert Octal number (65)8 to Binary number ( )2
| Steps | Description | Solution |
|---|---|---|
| 1 | Write down the octal number | (65)8 |
| 2 | Group all the digits in sets of three starting from the LSB (far right). Add zeros to the left of the last digit if there aren’t enough digits to make a set of three. Use the table below to convert each set of three into an octal digit.  | (6)8 = (110)2 (5)8 = (101)2 110 101 |
| 3 | Group each value of step 2 to make a binary number | (65)8 = (110101)2 |
Octal to Hexadecimal Converter
What is Hexadecimal Number? The number to the base 16 is called Hexadecimal numbers. It uses the numbers from 0 to 9, A, B, C, D, E, and F. There are mainly two ways to convert octal number to hexadecimal number.
Indirect Method
In indirect method first we need to convert octal number to decimal number then we can convert that decimal number to hexadecimal number.
For Example
Convert Octal number (65)8to Hexadecimal number ( )16
A) First, we convert Octal number (65)8to Decimal number ( )10, we use the Multiplication method. Octal to Decimal Converter
B) Secondly, we convert Decimal number ( )10 to Hexadecimal number ( )16, we use the Division method.
| Steps | Description | Solution |
|---|---|---|
| 1 | Divide decimal number by 16 until quotient is 0. | 53/16 = 3 Remainder is 5 3/16 = 0 Remainder is 3 |
| 2 | The last remainder obtained from the division is the most significant bit (MSB) of the binary number. Hence arrange the number from the most significant bit (MSB) to the least significant bit (LSB). Read from the bottom (MSB) to top (LSB) as 35. | (53)10 = (35)16 |
Octal number (65)8to Hexadecimal number (35)16
Direct Method
In this method, we grouped octal number and replace their equivalent hexadecimal number. To get hexadecimal number of given octal number, first we have to convert octal number into its 3 bit binary equivalent and then convert binary number into its hexadecimal equivalent.
For Example
Convert Octal number (65)8 to Hexadecimal number ( )16
| Steps | Description | Solution |
|---|---|---|
| 1 | Write down the octal number | (65)8 |
| 2 | Group all the digits in sets of three starting from the LSB (far right). | (6)8 = (110)2 (5)8 = (101)2 |
| 3 | Group each value of step 2 to make a binary number. | (65)8 = (110101)2 |
| 4 | Now convert the binary number from step 3 to hexadecimal by grouping all the digits of the binary in sets of four starting from LSB. Add zeros to the left of the last digit if there aren’t enough digits to make a set of four. | 0011 0101 |
| 5 | Convert each group of four to the corresponding hexadecimal (use the table below) | 0011 = 3 0101 = 5 (65)8 = (35)16 |