Question

The binary equivalent of $ (222)_3 $ is

• A. 11010
• B. 11001
• C. 10101
• D. 11101

Hint:

To convert a number from base 3 to binary, first convert it to decimal and then from decimal to binary.

Answer 1

The Correct Option is A

First, convert \( (222)_3 \) to decimal: \[ (222)_3 = 2 \times 3^2 + 2 \times 3^1 + 2 \times 3^0 = 2 \times 9 + 2 \times 3 + 2 \times 1 = 18 + 6 + 2 = 26. \] Now convert \( 26 \) to binary: \[ 26_{10} = 11010_2. \]
Thus, the binary equivalent is \( 11010 \).