Conversion of Binary to other base number system like conversion of Decimal to Binary Conversion, Decimal to Octal Conversion, and Decimal to Hexadecimal Conversion.
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.
Conversion of Decimal Number to Binary Number
Procedure
- Divide the decimal number by 2, noting the remainder.
- Continue to divide the quotient by 2 until there is nothing left, keeping track of the remainders from each step.
- List the remainder values in reverse order to find the number’s binary equivalent.
For Example
To Convert Decimal number (21)10 to Binary number ( )2, we use Division method.
| Steps | Description | Solution |
|---|---|---|
| 1 | Divide the decimal number by 2 until the quotient is 0. | 21/2 = 10 Remainder is 1 10/2 = 5 Remainder is 0 5/2 = 2 Remainder is 1 2/2 = 1 Remainder is 0 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 the top (LSB) as 10101 | (21)10 = (10101)2 |
Conversion of Decimal Number to Octal Number
Procedure
- Divide the decimal number by 8, noting the remainder.
- Continue to divide the quotient by 8 until there is nothing left, keeping the track of the remainders from each step.
- List the remainder values in reverse order to find the number’s octal equivalent.
For Example
To Convert Decimal number (2)10 to Octal number ( )8, we use Division method.
| Steps | Description | Solution |
|---|---|---|
| 1 | Divide the decimal number by 8 until the quotient is 0. | 2/8 = 0 Remainder is 2 |
| 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 the top (LSB) as 2. | (2)10 = (2)8 |
Conversion of Decimal Number to Hexadecimal Number
Procedure
- Divide the decimal number by 16, noting the remainder.
- Continue to divide the quotient by 16 until there is nothing left, keeping track of the remainders from each step.
- List the remainder values in reverse order to find the number’s hexadecimal equivalent.
For Example
To Convert Decimal number (14)10 to Hexadecimal number ( )16, we use Division method.
| Steps | Description | Solution |
|---|---|---|
| 1 | Divide the decimal number by 16 until the quotient is 0. | 14/16 = 0 Remainder is 14 |
| 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 the top (LSB) as 14. E is the hexadecimal equivalent of decimal number 14. | (14)10 = (E)8 |