100101011

100101011 is a nine‑digit binary number that represents the decimal value 299. In base‑2 notation the digits are interpreted as powers of two, beginning with the least significant bit on the right. The value can be calculated as 1×2⁸ + 0×2⁷ + 0×2⁶ + 1×2⁵ + 0×2⁴ + 1×2³ + 0×2² + 1×2¹ + 1×2⁰, which equals 256 + 0 + 0 + 32 + 0 + 8 + 0 + 2 + 1 = 299. The binary string is also equivalent to the hexadecimal representation 0x12B in most systems.

The number 299 has several mathematical properties that can be relevant in computer science and number theory. It is a composite number because it can be factored into 13 and 23. It is an odd number and is not a prime, a perfect square, or a perfect cube. In binary, 100101011 has exactly five ones and four zeros, giving it a Hamming weight of five.

Binary numbers such as 100101011 appear in computing contexts where compact representation of data is needed, such as flags in a 64‑bit processor register, or as part of encoded messages in embedded systems. The pattern also illustrates how nine‑bit binary can encode values up to 511, which is sufficient for representing characters in many legacy character sets that extend beyond the basic ASCII range.

In digital logic design, a 9‑bit vector might use the pattern 100101011 to configure a mode of operation, to indicate a specific instruction opcode, or as a test vector for verification of combinational circuits. It is common in hardware description languages such as VHDL or Verilog to see such explicit binary constants annotated with a prefix (e.g., “9'b100101011”).

Because the binary string maps directly to a decimal integer, it can be easily converted to other bases: as a decimal number it is 299; as a hexadecimal number it is 0x12B; and as an octal number it is 0o453. These conversions are often used for documentation, debugging, or when interfacing with systems that prefer one base over another.

Overall, 100101011 serves as a concise example of binary representation, base conversion, and basic numerical properties that are commonly encountered in both theoretical and applied computing.