Question

How to convert 76 octal to binary?

Answer 1

To convert an octal number to binary, you can follow these steps:

1. **Understand the Octal System:**
   - Octal (base-8) uses digits from 0 to 7.
   - Each octal digit can be directly converted to a 3-digit binary number (since \(2^3 = 8\)).

2. **Convert Each Octal Digit to Binary:**
   - Write down the binary equivalent of each octal digit. Here’s a quick reference for each digit from 0 to 7:
     - \(0_{8}\) = \(000_{2}\)
     - \(1_{8}\) = \(001_{2}\)
     - \(2_{8}\) = \(010_{2}\)
     - \(3_{8}\) = \(011_{2}\)
     - \(4_{8}\) = \(100_{2}\)
     - \(5_{8}\) = \(101_{2}\)
     - \(6_{8}\) = \(110_{2}\)
     - \(7_{8}\) = \(111_{2}\)

3. **Apply the Conversion to Each Digit:**
   - For the octal number \(76_{8}\):
     - The digit \(7\) in octal converts to \(111_{2}\).
     - The digit \(6\) in octal converts to \(110_{2}\).

4. **Combine the Binary Values:**
   - Concatenate the binary values from each digit without any spaces.
   - So, \(76_{8}\) becomes \(111_{2}\) followed by \(110_{2}\).

5. **Final Binary Result:**
   - Putting it together, \(76_{8}\) converts to \(111110_{2}\).

So, the octal number \(76_{8}\) is \(111110_{2}\) in binary.

Answer 2

To convert the octal number 76 to binary, follow these steps:

1. **Convert each octal digit to its 3-bit binary equivalent:**
   - Octal 7 in binary is `111`.
   - Octal 6 in binary is `110`.

2. **Combine these binary equivalents:**
   - The octal number 76 is represented as `111 110` in binary.

So, the binary equivalent of the octal number 76 is `111110`.