1100100001

1100100001 is a binary number. In the decimal system, it translates to the value 801. Binary is a base-2 numeral system that uses only two symbols, typically 0 and 1, to represent numbers. Each digit in a binary number, known as a bit, represents a power of two. Starting from the rightmost digit as 2^0, the powers increase by one for each position to the left.

To convert 1100100001 to decimal, we can multiply each bit by its corresponding power of two and sum the results. The leftmost '1' is in the 2^9 position, the next '1' is in the 2^4 position, and the rightmost '1' is in the 2^0 position. Therefore, the calculation is (1 * 2^9) + (1 * 2^4) + (1 * 2^0) = 512 + 16 + 1 = 529. My apologies, the previous calculation was incorrect. Let's re-evaluate.

The binary number 1100100001 has 10 digits. From right to left, these digits correspond to the powers of 2 starting from 2^0.

The positions and their corresponding powers of 2 are:

1 (2^9) + 1 (2^8) + 0 (2^7) + 0 (2^6) + 1 (2^5) + 0 (2^4) + 0 (2^3) + 0 (2^2) + 0 (2^1) + 1 (2^0)

Calculating this sum:

(1 * 512) + (1 * 256) + (0 * 128) + (0 * 64) + (1 * 32) + (0 * 16) + (0 * 8) + (0 * 4) + (0 * 2) + (1 * 1)

= 512 + 256 + 0 + 0 + 32 + 0 + 0 + 0 + 0 + 1

= 801

Therefore, the binary number 1100100001 is equal to 801 in the decimal system. Binary numbers are fundamental to computer science, as digital computers use binary to represent and process all data.