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Binary and octal are both numeral systems used to represent numbers. They are different from the more commonly used decimal system, which is based on ten digits (0 to 9). Here’s a brief explanation of binary and octal:
Binary is a base-2 numeral system, which means it uses only two symbols to represent numbers: 0 and 1. Each digit in a binary number is referred to as a “bit” (short for binary digit). Binary is fundamental in computer science and digital electronics since computers store and process data using binary code.
Octal is a base-8 numeral system, which means it uses eight symbols to represent numbers: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit in an octal number is referred to as an “octit” (short for octal digit).
| Binary | Octal |
| 000 | 0 |
| 001 | 1 |
| 010 | 2 |
| 011 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
To convert a binary number to octal, follow these steps: Group the binary digits into sets of three, starting from the rightmost digit. If there are any leading groups with less than three digits, pad them with zeros on the left. Write down the corresponding octal digit for each group of three binary digits. Concatenate the octal digits to get the final octal representation.
To convert 1010111100 from binary to octal: Step 1: Group the binary digits into sets of three (leading zeros added): 001 | 010 | 111 | 100 Step 2: Write down the corresponding octal digit for each group: 1 | 2 | 7 | 4 Step 3: Concatenate the octal digits: 1274
To convert 1101 from binary to octal: Step 1: Group the binary digits into sets of three (leading zero added): 001 | 101 Step 2: Write down the corresponding octal digit for each group: 1 | 5 Step 3: Concatenate the octal digits: 15
To convert 10010110 from binary to octal: Step 1: Group the binary digits into sets of three (leading zeros added): 010 | 010 | 110 Step 2: Write down the corresponding octal digit for each group: 2 | 2 | 6 Step 3: Concatenate the octal digits: 226
To convert 11001 from binary to octal: Step 1: Group the binary digits into sets of three (leading zero added): 011 | 001 Step 2: Write down the corresponding octal digit for each group: 3 | 1 Step 3: Concatenate the octal digits: 31
To convert 100111010 from binary to octal: Step 1: Group the binary digits into sets of three (leading zero added): 100 | 111 | 010 Step 2: Write down the corresponding octal digit for each group: 4 | 7 | 2 Step 3: Concatenate the octal digits: 472
To convert 101101 from binary to octal: Step 1: Group the binary digits into sets of three (leading zero added): 101 | 101 Step 2: Write down the corresponding octal digit for each group: 5 | 5 Step 3: Concatenate the octal digits: 55