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Rem 2
1
सूत्र
Number Base Conversion
Method: Repeated Division
To convert decimal to base b: 1. Divide n by b, record the remainder 2. Replace n with the quotient 3. Repeat until n = 0 4. Read remainders from bottom to top
Common Bases
हल किया गया उदाहरण
Analyze the number 255 in different bases.
- 01255 in binary: 11111111 (8 binary digits)
- 02255 in octal: 377 (last digit: 255 mod 8 = 7)
- 03255 in hex: FF (last digit: 255 mod 16 = 15 = F)
- 04Bits needed: floor(log2(255))+1 = 8
अक्सर पूछे जाने वाले प्रश्न
Why are number bases important?
Different bases are used in different contexts: binary for computers, octal for Unix permissions, hexadecimal for memory addresses and colors, decimal for everyday use.
How do I convert from decimal to binary?
Repeatedly divide by 2 and record remainders. Read the remainders from bottom to top. For example, 13 → 6r1 → 3r0 → 1r1 → 0r1, so 13 = 1101 in binary.
Why is 255 special in computing?
255 is the largest 8-bit unsigned integer (11111111 in binary, FF in hex). It is the maximum value for each channel in 24-bit RGB color codes.
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