Mathematiques
Calculatrice vérifiée avec une formule transparente
Decimal to Binary Calculator.
Converts a non-negative decimal integer into its binary (base-2) representation.
Vos entrées
Comment ça marche
- 1
Divide the decimal number by 2 and record the remainder (0 or 1).
- 2
Divide the quotient by 2 again and record the next remainder.
- 3
Repeat until the quotient becomes 0.
- 4
Read the remainders from bottom to top to get the binary number.
floor(decimal) % 2 + 10 * (floor(decimal / 2) % 2) + 100 * (floor(decimal / 4) % 2) + 1000 * (floor(decimal / 8) % 2) + 10000 * (floor(decimal / 16) % 2) + 100000 * (floor(decimal / 32) % 2) + 1000000 * (floor(decimal / 64) % 2) + 10000000 * (floor(decimal / 128) % 2) + 100000000 * (floor(decimal / 256) % 2) + 1000000000 * (floor(decimal / 512) % 2) + 10000000000 * (floor(decimal / 1024) % 2) + 100000000000 * (floor(decimal / 2048) % 2) + 1000000000000 * (floor(decimal / 4096) % 2) + 10000000000000 * (floor(decimal / 8192) % 2) + 100000000000000 * (floor(decimal / 16384) % 2) + 1000000000000000 * (floor(decimal / 32768) % 2) + 10000000000000000 * (floor(decimal / 65536) % 2) + 100000000000000000 * (floor(decimal / 131072) % 2) + 1000000000000000000 * (floor(decimal / 262144) % 2) + 10000000000000000000 * (floor(decimal / 524288) % 2)Questions fréquentes
How do I convert a decimal number to binary manually?
Repeatedly divide the number by 2, writing down the remainder each time. Continue until the quotient is 0, then read the remainders in reverse order.
What is the binary representation of 0?
0 in binary is simply 0.
Can this calculator handle very large numbers?
It works for non-negative integers up to about 1,000,000, which covers most everyday needs.
Explorer cette catégorie de calculatrices
Résultats
Formule vérifiéeBinary
101 010
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Comment ça marche
Converts a non-negative decimal integer into its binary (base-2) representation.
- Divide the decimal number by 2 and record the remainder (0 or 1).
- Divide the quotient by 2 again and record the next remainder.
- Repeat until the quotient becomes 0.
- Read the remainders from bottom to top to get the binary number.
Formules
Les mathématiques derrière cette calculatrice, écrites pour que vous puissiez vérifier le résultat.
Division by 2 method
Each division step extracts the least significant bit of the binary representation.
Example:
Input: N = 13
Calculation: 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1
Result: Binary: 1101
Cas d'utilisation réels
Où ce calcul apparaît dans la vie quotidienne.
Computer science education
Understanding how numbers are stored in binary is fundamental to programming and digital logic.
Example: Converting IP addresses or memory addresses.
Digital electronics
Designing circuits that use binary signals often requires converting decimal values to binary.
Example: Setting a binary switch configuration.
Data encoding
Binary representation is used in encoding schemes like ASCII and Unicode.
Example: Converting character codes to binary.
Conseils et erreurs courantes
Tips
- For quick conversion, memorize powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, etc.
- Check your result by converting back: multiply each binary digit by its power of 2 and sum.
- Use leading zeros if you need a fixed-width binary representation (e.g., 8 bits).
- For negative numbers, use two's complement, but this calculator handles only non-negative integers.
Common Mistakes to Avoid
- Forgetting to read remainders in reverse order.
- Stopping too early when the quotient is not yet 0.
- Confusing the order of bits: the last remainder is the most significant bit.
Hypothèses et limites
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.