Conversion from one number base to another is a common task in mathematics and computer science. In this article, we will explore the methods and techniques for converting numbers from one base to another.
CONVERSION BETWEEN BINARY, OCTAL, AND HEXADECIMAL NUMBER SYSTEM
Binary, octal, and hexadecimal are all number systems that are widely used in computer science and digital electronics. The base of binary is 2, octal is 8, and hexadecimal is 16. To convert numbers between these bases, we need to know the place values and the digits used in each system.
BINARY TO OCTAL/HEXADECIMAL
To convert a binary number to octal or hexadecimal, we can first divide the binary number into groups of three or four digits, respectively. We can then convert each group to its corresponding octal or hexadecimal digit. The table below shows the conversion of binary digits to octal and hexadecimal digits:
| Binary | Octal | Hexadecimal |
|---|---|---|
| 000 | 0 | 0 |
| 001 | 1 | 1 |
| 010 | 2 | 2 |
| 011 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
To illustrate, let’s convert the binary number 101101010 to octal and hexadecimal:
Binary to Octal
We group the binary number into groups of three digits: 101 101 010. We then convert each group to its corresponding octal digit: 5 5 2. The octal representation of 101101010 is therefore 552.
Binary to Hexadecimal
We group the binary number into groups of four digits: 0001 0110 1010. We then convert each group to its corresponding hexadecimal digit: 1 6 A. The hexadecimal representation of 101101010 is therefore 16A.
See also: CONVERSION FROM OTHER BASES TO BASE 10 WITH VIDEO – NUMBER BASES
OCTAL/HEXADECIMAL TO BINARY
To convert an octal or hexadecimal number to binary, we can simply convert each digit to its corresponding binary representation. The table below shows the conversion of octal and hexadecimal digits to binary:
| Octal | Binary | Hexadecimal | Binary |
|---|---|---|---|
| 0 | 000 | 0 | 0000 |
| 1 | 001 | 1 | 0001 |
| 2 | 010 | 2 | 0010 |
| 3 | 011 | 3 | 0011 |
| 4 | 100 | 4 | 0100 |
| 5 | 101 | 5 | 0101 |
| 6 | 110 | 6 | 0110 |
| 7 | 111 | 7 | 0111 |
| 8 | 1000 | ||
| 9 | 1001 | ||
| A | 1010 | ||
| B | 1011 | ||
| C | 1100 | ||
| D | 1101 | ||
| E | 1110 | ||
| F | 1111 |
To illustrate, let’s convert the octal number 247 to binary and the hexadecimal number ABCD to binary:
Octal to Binary
We convert each octal digit to its corresponding binary representation: 2 4 7 becomes 010 100 111. The binary representation of 247 is therefore 010100111.
Hexadecimal to Binary
We convert each hexadecimal digit to its corresponding binary representation: A B C D becomes 1010 1011 1100 1101. The binary representation of ABCD is therefore 1010101111001101.
Still unclear, watch the detailed video below
CONCLUSION
Converting between different number bases is a fundamental skill in mathematics and computer science. By understanding the place values and digits used in each system, we can use the appropriate method to convert numbers from one base to another. Whether we are working with binary, octal, hexadecimal, or other non-digital bases, the basic principles of conversion remain the same.
Leave a Reply