What is the decimal value of the binary number 010101001?

• A. 169
• B. 128
• C. 101
• D. 249

Answer: (A)

Binary to decimal conversion relies on summing powers of two for every position that has a 1. Each bit represents a value 2^k, where k is its position index from the right starting at 0.

For the number 010101001, there are nine bits, so the rightmost bit is 2^0 and the leftmost is 2^8. The bits that are 1 occur at positions 7, 5, 3, and 0. Add those contributions: 2^7 (128) + 2^5 (32) + 2^3 (8) + 2^0 (1) = 169.

That matches the decimal value of this binary pattern. The other numbers wouldn’t fit because they don’t equal the sum of those specific powers of two.