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Number bases

Converting between decimal, binary, octal and hexadecimal.

A base-b number is a sum of powers of b. To convert from decimal, divide by b repeatedly; the remainders, read from the last to the first, are the digits. Binary (base 2) and hexadecimal (base 16) are how computers store every number you see.

Иштөө мисалы · 255 to binary

Number-Theory · Number-Bases

255 to binary

255,\ 2

Аткаруу

  1. 255_{10} \to \text{base } 2

    Repeatedly divide by 2; the remainders, read bottom-up, are the digits.

  2. 255 = 127 \times 2 + 1

    remainder 1

  3. 127 = 63 \times 2 + 1

    remainder 1

  4. 63 = 31 \times 2 + 1

    remainder 1

  5. 31 = 15 \times 2 + 1

    remainder 1

  6. 15 = 7 \times 2 + 1

    remainder 1

  7. 7 = 3 \times 2 + 1

    remainder 1

  8. 3 = 1 \times 2 + 1

    remainder 1

  9. 1 = 0 \times 2 + 1

    remainder 1

Жауап
255_{10} = 11111111_{2}

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Бул жерде колдонулган символдор

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Кантип: Number bases

  1. Repeatedly divide by 2; the remainders, read bottom-up, are the digits.
  2. remainder 1
  3. remainder 1
  4. remainder 1
  5. remainder 1
  6. remainder 1
  7. remainder 1
  8. remainder 1

Кээ бирлердин суроосу

Why are primes so important?

Every integer factors into primes in exactly one way, so primes are the atoms of multiplication. Cryptography relies on that factoring being easy to state and hard to do.

How do I tell whether a big number is prime?

Trial division up to the square root works for small numbers. For large ones, probabilistic tests (Miller-Rabin) give an answer that is wrong with negligible probability, and deterministic tests (AKS) exist but are slower.

Кээ бирлери Number Theory

Prime factorisationPrime numbersGCD and LCMModular arithmeticDivisorsSequencesDiophantine equationsFermat's little theorem and Euler's theoremRSA: cryptography from number theory