To convert 101001000000111 from binary to decimal, we multiply each digit by its corresponding power of 2 and sum the results. Starting from the rightmost digit:
My apologies, there was a miscalculation in the previous conversion. Let's re-evaluate the binary number 101001000000111.
Summing these values: 1 + 2 + 4 + 0 + 0 + 0 + 0 + 0 + 256 + 0 + 0 + 2048 + 0 + 8192 + 0 + 32768 = 43271.
The binary number 101001000000111, when converted to its base-10 equivalent, is 43271. This number consists of 16 binary digits. In the binary system, each digit's place value is a power of 2. Starting from the rightmost digit, the place values are 2^0, 2^1, 2^2, and so on, up to 2^15 for the leftmost digit. To find the decimal value, we multiply each binary digit by its corresponding place value and sum the results. The digits that are '1' contribute to the sum, while the digits that are '0' do not. Specifically, the digits at positions corresponding to 2^0, 2^1, 2^2, 2^8, 2^11, 2^13, and 2^15 are '1', and these powers of 2 are 1, 2, 4, 256, 2048, 8192, and 32768 respectively. Their sum is 43271.