Binary to Octal and Octal to Binary Conversion

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1. Binary to Octal Conversion

The octal number system (Base-8) uses 8 digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each octal digit corresponds to a group of 3 binary digits (bits).

Steps for Binary to Octal Conversion

  1. Group the binary digits into triplets (sets of 3 bits) from right to left.
  2. Convert each triplet into its octal equivalent.
  3. Write the final octal number.

Example 1: Convert 110101₂ to Octal

Step 1: Group in triplets from right to left

110101 → (110) (101)

Step 2: Convert each triplet to octal

  • 110₂ = 6₈
  • 101₂ = 5₈

Step 3: Write the octal number

110101₂ = 65₈

Example 2: Convert 101100110₂ to Octal

Step 1: Group into triplets

101100110 → (101) (100) (110)

Step 2: Convert to octal

  • 101₂ = 5₈
  • 100₂ = 4₈
  • 110₂ = 6₈

Step 3: Final octal number

101100110₂ = 546₈

2. Octal to Binary Conversion

Each octal digit corresponds to three binary digits.

Steps for Octal to Binary Conversion

  1. Write each octal digit as a 3-bit binary equivalent.
  2. Combine the binary groups to form the binary number.

Example 3: Convert 75₈ to Binary

Step 1: Convert each digit to binary

  • 7₈ = 111₂
  • 5₈ = 101₂

Step 2: Combine the binary numbers

75₈ = 111101₂

Example 4: Convert 236₈ to Binary

Step 1: Convert each digit to binary

  • 2₈ = 010₂
  • 3₈ = 011₂
  • 6₈ = 110₂

Step 2: Combine the binary groups

236₈ = 010011110₂

MCQs on Binary-Octal Conversion

1. What is the octal equivalent of 101010₂?

a) 42₈

b) 50₈

c) 52₈

d) 54₈

✅ Answer: c) 52₈

2. Convert 110011₂ to octal.

a) 63₈

b) 73₈

c) 61₈

d) 64₈

✅ Answer: a) 63₈

3. Convert octal 57₈ to binary.

a) 110111₂

b) 101111₂

c) 111011₂

d) 110101₂

✅ Answer: b) 101111₂

4. Convert 23₈ to binary.

a) 101010₂

b) 010011₂

c) 011011₂

d) 100101₂

✅ Answer: b) 010011₂

5. What is the binary equivalent of octal 6?

a) 100₂

b) 101₂

c) 110₂

d) 111₂

✅ Answer: c) 110₂

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