1101 can refer to the integer one thousand one hundred one, the character string "1101" in other bases (notably binary), or the historical year 1101 CE. Each sense appears in different fields: mathematics and number theory, digital computing where base notation matters, and medieval history for the early twelfth century. The entries below separate these senses and highlight the most commonly referenced properties and contexts.

Mathematical properties

As a decimal integer, 1101 is an odd composite number. Its prime factorization is 3 × 367, so it is a semiprime with exactly four positive divisors: 1, 3, 367 and 1101. It is not a square or a cube. The sum of its decimal digits is 1+1+0+1 = 3, which explains immediate divisibility by 3. In modular terms 1101 ≡ 1 (mod 2) and 1101 ≡ 0 (mod 3).

Representations and computing

Numbers change value when interpreted in different bases, so the symbol sequence "1101" must be disambiguated. In binary (base 2) the string "1101" equals thirteen in decimal; in hexadecimal that 4‑bit binary pattern is written as D. Conversely, the decimal number 1101 converts to binary as 10001001101 (an 11‑bit pattern) and to hexadecimal as 0x44D. In digital electronics and bitwise operations, short patterns such as 1101 often represent flags or nibble values; that pattern has three ones, so it has odd parity.

Year 1101 (Common Era)

The year 1101 falls in the early twelfth century, a period shaped by the aftermath of the First Crusade and political consolidation in western Europe. Two widely noted occurrences connected to that year are the so‑called Crusade of 1101, a series of reinforcements and smaller expeditions that largely failed to achieve the aims of the First Crusade, and political settlement in England known as the Treaty of Alton, which involved King Henry I and his brother Robert Curthose. More broadly, 1101 sits within the era of Norman rule in England, Seljuk influence in Anatolia, and the Song dynasty in China.

Uses, examples, and distinctions

  • In mathematics and recreational number theory, 1101 is an elementary example of a semiprime used to illustrate factorization properties.
  • In computing, the four‑digit binary string 1101 commonly appears as a nibble value, test pattern, mask, or small opcode fragment; care must be taken whether those digits are read as binary or as a decimal numeral.
  • As a calendar year it is shorthand for events and documents dated 1101 CE; historians always contextualize it within the greater political and religious movements of the twelfth century.

When encountering 1101, identify whether the context is numeric (decimal value 1101), symbolic (the characters "1101" in another radix), or historical (the year 1101 CE) to avoid confusion. Each reading has simple, practical conversions and widely known associations that make the distinction straightforward in most usages.