0b1000001010

0b1000001010 is a binary number that represents the decimal value 522. The prefix "0b" indicates that the following digits are expressed in base-2 numeral system, which uses only two symbols: 0 and 1. Each digit position represents a power of 2, starting from 2^0 on the right side.

When converting 0b1000001010 to decimal, the calculation involves multiplying each binary digit by its corresponding power of 2 and summing the results. From right to left, the positions represent 2^0, 2^1, 2^2, and so on. In this case, the binary digits 1 appear in positions corresponding to 2^1, 2^3, and 2^9, resulting in the calculation: (1×2^1) + (1×2^3) + (1×2^9) = 2 + 8 + 512 = 522.

In octal notation, 0b1000001010 converts to 1012, while in hexadecimal it becomes 0x20A. The binary representation contains 10 digits, with 3 ones and 7 zeros, making it a relatively sparse binary number.

Binary numbers form the foundation of digital computing systems, where each bit represents an on (1) or off (0) state in electronic circuits. The number 0b1000001010 could represent various data types in computing contexts, including integers, memory addresses, or bit flags, depending on the specific application and system architecture.

In terms of bit manipulation, this binary number has its least significant set bit at position 1 and its most significant set bit at position 9. The number requires 10 bits for storage in binary form and would typically be represented using at least a 16-bit integer container in most computing systems.