1111010100001

1111010100001 is a binary numeral consisting of 13 bits. It can function as a binary constant in digital logic, programming, or theoretical discussions of number representations.

Numerical representations and value: Interpreted in base-2, the string equals the decimal number 7841. In hexadecimal, it is 0x1EA1. This value arises from summing the powers of two corresponding to the positions of the 1 bits: 2^12 + 2^11 + 2^10 + 2^9 + 2^7 + 2^5 + 2^0 = 7841.

Pattern and properties: The bitstring contains seven 1s and six 0s. It begins with a run of four consecutive 1s, followed by alternating bits and a final 1. If padded with leading zeros to form a 16-bit group, it corresponds to 0001 1110 1010 0001, which confirms the hexadecimal value 0x1EA1.

Primality and relevance: The decimal value 7841 is a prime number, meaning it has no positive divisors other than 1 and itself. As a fixed binary pattern, 1111010100001 can be used as a simple test vector or seed in computing contexts where a deterministic, nontrivial bit pattern is desirable.

In other bases and applications: Beyond binary and hexadecimal representations, the string is primarily of interest as a numeric constant or pattern in discussions of binary arithmetic, digital design, and encoding. See also binary numeral systems and hexadecimal notation.