1000001101

1000001101 is a binary number. In the decimal system, this binary representation converts to 653. Binary numbers are the foundation of modern computing, using only two digits, 0 and 1, to represent all data. Each position in a binary number represents a power of two, starting from the rightmost digit as 2 to the power of 0, then 2 to the power of 1, and so on.

To convert 1000001101 to decimal, we multiply each binary digit by its corresponding power of two and sum the results. Starting from the right:

1 * 2^0 = 1 * 1 = 1

0 * 2^1 = 0 * 2 = 0

1 * 2^2 = 1 * 4 = 4

1 * 2^3 = 1 * 8 = 8

0 * 2^4 = 0 * 16 = 0

0 * 2^5 = 0 * 32 = 0

0 * 2^6 = 0 * 64 = 0

0 * 2^7 = 0 * 128 = 0

0 * 2^8 = 0 * 256 = 0

1 * 2^9 = 1 * 512 = 512

Summing these values: 512 + 0 + 0 + 0 + 0 + 8 + 4 + 0 + 1 = 625.

Wait, let me recheck that calculation.

1000001101

1 * 2^0 = 1

0 * 2^1 = 0

1 * 2^2 = 4

1 * 2^3 = 8

0 * 2^4 = 0

0 * 2^5 = 0

0 * 2^6 = 0

0 * 2^7 = 0

0 * 2^8 = 0

1 * 2^9 = 512

Summing: 512 + 8 + 4 + 1 = 525.

My apologies, there was an error in my previous calculation. The correct decimal equivalent of the binary number 1000001101 is 525. This number, like all binary numbers, is a fundamental building block for how computers store and process information.