c# - What is 0x10 in decimal?

Question

I have the following code:

SN.get_Chars(5)

SN is a string so this should give the 5th Char. Ok!

Now I have another code but: SN.get_Chars(0x10)

I wonder what 0x10 is? Is it a number? If it's so, then what is it in decimal notation?

Answer 1

0xNNNN (not necessarily four digits) represents, in C at least, a hexadecimal (base-16 because 'hex' is 6 and 'dec' is 10 in Latin-derived languages) number, where N is one of the digits 0 through 9 or A through F (or their lower case equivalents, either representing 10 through 15), and there may be 1 or more of those digits in the number. The other way of representing it is NNNN₁₆.

It's very useful in the computer world as a single hex digit represents four bits (binary digits). That's because four bits, each with two possible values, gives you a total of 2 x 2 x 2 x 2 or 16 (2⁴) values. In other words:

  _____________________________________bits____________________________________
 /                                                                             
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
| bF | bE | bD | bC | bB | bA | b9 | b8 | b7 | b6 | b5 | b4 | b3 | b2 | b1 | b0 |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
 \_________________/ \_________________/ \_________________/ \_________________/ 
      Hex digit           Hex digit           Hex digit           Hex digit

A base-X number is a number where each position represents a multiple of a power of X.

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In base 10, which we humans are used to, the digits used are 0 through 9, and the number 7304₁₀ is:

• (7 x 10³) = 7000₁₀ ; plus
• (3 x 10²) = 300₁₀ ; plus
• (0 x 10¹) = 0₁₀ ; plus
• (4 x 10⁰) = 4₁₀ ; equals 7304.

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In octal, where the digits are 0 through 7. the number 754₈ is:

• (7 x 8²) = 448₁₀ ; plus
• (5 x 8¹) = 40₁₀ ; plus
• (4 x 8⁰) = 4₁₀ ; equals 492₁₀.

Octal numbers in C are preceded by the character 0 so 0123 is not 123 but is instead (1 * 64) + (2 * 8) + 3, or 83.

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In binary, where the digits are 0 and 1. the number 1011₂ is:

• (1 x 2³) = 8₁₀ ; plus
• (0 x 2²) = 0₁₀ ; plus
• (1 x 2¹) = 2₁₀ ; plus
• (1 x 2⁰) = 1₁₀ ; equals 11₁₀.

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In hexadecimal, where the digits are 0 through 9 and A through F (which represent the "digits" 10 through 15). the number 7F24₁₆ is:

• (7 x 16³) = 28672₁₀ ; plus
• (F x 16²) = 3840₁₀ ; plus
• (2 x 16¹) = 32₁₀ ; plus
• (4 x 16⁰) = 4₁₀ ; equals 32548₁₀.

Your relatively simple number 0x10, which is the way C represents 10₁₆, is simply:

• (1 x 16¹) = 16₁₀ ; plus
• (0 x 16⁰) = 0₁₀ ; equals 16₁₀.

As an aside, the different bases of numbers are used for many things.

• base 10 is used, as previously mentioned, by we humans with 10 digits on our hands.
• base 2 is used by computers due to the relative ease of representing the two binary states with electrical circuits.
• base 8 is used almost exclusively in UNIX file permissions so that each octal digit represents a 3-tuple of binary permissions (read/write/execute). It's also used in C-based languages and UNIX utilities to inject binary characters into an otherwise printable-character-only data stream.
• base 16 is a convenient way to represent four bits to a digit, especially as most architectures nowadays have a word size which is a multiple of four bits.
• base 64 is used in encoding mail so that binary files may be sent using only printable characters. Each digit represents six binary digits so you can pack three eight-bit characters into four six-bit digits (25% increased file size but guaranteed to get through the mail gateways untouched).
• as a semi-useful snippet, base 60 comes from some very old civilisation (Babylon, Sumeria, Mesopotamia or something like that) and is the source of 60 seconds/minutes in the minute/hour, 360 degrees in a circle, 60 minutes (of arc) in a degree and so on [not really related to the computer industry, but interesting nonetheless].
• as an even less-useful snippet, the ultimate question and answer in The Hitchhikers Guide To The Galaxy was "What do you get when you multiply 6 by 9?" and "42". Whilst same say this is because the Earth computer was faulty, others see it as proof that the creator has 13 fingers :-)