In binary notation, the value 100000 represents which decimal number?

In binary notation, the value 100000 represents which decimal number?

• A. 32
• B. 8
• C. 64
• D. 16

Answer: (A)

In binary, each digit represents a power of two, with the rightmost bit as 2^0. To find the decimal value, add the powers corresponding to the positions where there is a 1. For 100000, the only 1 is in the 2^5 position, so the value is 2^5 = 32. Therefore, the decimal number is 32. For comparison, 8 is 1000 (2^3), 16 is 10000 (2^4), and 64 is 1000000 (2^6).

In binary, each digit represents a power of two, with the rightmost bit as 2^0. To find the decimal value, add the powers corresponding to the positions where there is a 1. For 100000, the only 1 is in the 2^5 position, so the value is 2^5 = 32. Therefore, the decimal number is 32. For comparison, 8 is 1000 (2^3), 16 is 10000 (2^4), and 64 is 1000000 (2^6).