0001101000010000
The string "0001101000010000" is a binary representation of a number. In binary, each digit represents a power of two, starting from the rightmost digit as 2^0, the next as 2^1, and so on.
To convert "0001101000010000" to its decimal equivalent, we assign place values:
The rightmost '0' is in the 2^0 place (1).
The next '0' is in the 2^1 place (2).
The '0' is in the 2^2 place (4).
The '0' is in the 2^3 place (8).
The '1' is in the 2^4 place (16).
The '0' is in the 2^5 place (32).
The '0' is in the 2^6 place (64).
The '0' is in the 2^7 place (128).
The '1' is in the 2^8 place (256).
The '0' is in the 2^9 place (512).
The '1' is in the 2^10 place (1024).
The '0' is in the 2^11 place (2048).
The '0' is in the 2^12 place (4096).
The '0' is in the 2^13 place (8192).
The '0' is in the 2^14 place (16384).
The leftmost '0' is in the 2^15 place (32768).
Summing the values where there is a '1':
16 (from 2^4) + 256 (from 2^8) + 1024 (from 2^10) = 1300.
Therefore, the binary string "0001101000010000" represents the decimal number 1300. Binary representations are fundamental in computer