1001001000100

1001001000100 is a 13‑digit binary numeral that represents the decimal value 4 676. In binary notation each digit corresponds to a power of two, with the right‑most digit representing 2⁰. The conversion proceeds as follows: 1 × 2¹² + 0 × 2¹¹ + 0 × 2¹⁰ + 1 × 2⁹ + 0 × 2⁸ + 0 × 2⁷ + 1 × 2⁶ + 0 × 2⁵ + 0 × 2⁴ + 0 × 2³ + 1 × 2² + 0 × 2¹ + 0 × 2⁰ = 4 676.

The binary pattern consists of three occurrences of the sub‑sequence “100” followed by an extra “0100”. Such repeating structures are sometimes examined in digital signal processing and computer architecture when analyzing bit‑stream alignment or pattern detection. In hardware description languages the literal 0b1001001000100 may be used to initialise registers or memory locations for testing purposes.

From a mathematical perspective, the number lies between 2¹² = 4 096 and 2¹³ = 8 192, placing it in the lower half of the 13‑bit range. Its binary representation is not palindromic, but the distribution of ones (four in total) yields a Hamming weight of four, which can be relevant in error‑detecting codes that rely on parity checks.