1. **Problem:** Convert the octal number 102.3 (base 8) into binary. 2. **Formula and rules:** - Each octal digit corresponds to exactly 3 binary digits because $8 = 2^3$. - To convert, replace each octal digit with its 3-bit binary equivalent. 3. **Conversion steps:** - Octal number: 102.3 - Convert each digit: - $1_8 = 001_2$ - $0_8 = 000_2$ - $2_8 = 010_2$ - Fractional digit $3_8 = 011_2$ 4. **Combine:** - Integer part: $1 0 2_8 = 001 000 010_2$ - Fractional part: $.3_8 = .011_2$ 5. **Final binary number:** $$102.3_8 = 001000010.011_2 = 1000010.011_2$$ 6. **Explanation:** - We write the binary number without leading zeros in the integer part. - So the final answer is $1000010.011_2$.