I'm writing some code to convert an v4 ip stored in a string to a custom data type (a class with 4 integers in this case).
I was wondering if I should accept ips like the one I put in the title or only ips wiht no preceding zeros, let's see it with an example.
This two ips represent the same to us (humans) and for example windows network configuration accepts them:
192.56.2.1 and 192.056.2.01
But I was wondering if the second one is actually correct or not.
I mean, according to the RFC is the second ip valid?.
Thanks in advance.
Be careful, inet_addr(3) is one of Unix's standard API to translate a textual representation of IPv4 address into an internal representation, and it interprets 056 as an octal number:
http://pubs.opengroup.org/onlinepubs/9699919799/functions/inet_addr.html
All numbers supplied as parts in IPv4 dotted decimal notation may be decimal, octal, or hexadecimal, as specified in the ISO C standard (that is, a leading 0x or 0X implies hexadecimal; otherwise, a leading '0' implies octal; otherwise, the number is interpreted as decimal).
Its younger brothers like inet_ntop(3) and getaddrinfo(3) are all the same:
http://pubs.opengroup.org/onlinepubs/9699919799/functions/inet_ntop.html
http://pubs.opengroup.org/onlinepubs/9699919799/functions/getaddrinfo.html
Summary
Although such textual representations of IP addresses like 192.056.2.01 might be valid on all platforms, different OS interpret them differently.
This would be enough reason for me to avoid such a way of textual representation.
Pros
In decimal numerotation 056 is equals to 56 so why not?
Cons
0XX format is commonly used to octal numerotation
Whatever your decisions just put it on your documentation and it will be ok :)
Defining if it is correct or not depends on your implementation.
As you mentioned windows OS considers it correct because it removes any leading zeros when it resolves the IP.
So if in your program you set an appropriate logic, e.g every subset of the IP stored in your 4 integer class, without the leading zeros, it will be correct for your case too.
Textual Representation of IPv4 and IPv6 Addresses is an “Internet-Draft”,
which, I guess, is like an RFC wanna-be.
(Also, it expired a decade ago, on 2005-08-23,
and, apparently, has not been reissued,
so it’s not even close to being official.)
Anyway, in Section 2: History it says,
The original IPv4 “dotted octet” format was never fully defined in any RFC,
so it is necessary to look at usage,
rather than merely find an authoritative definition,
to determine what the effective syntax was.
The first mention of dotted octets in the RFC series is …
four dot-separated parts, each of which consists of
“three digits representing an integer value in the range 0 through 255”.
A few months later, [[IPV4-NUMB][3]] …
used dotted decimal format, zero-filling each encoded octet to three digits.
⋮
Meanwhile,
a very popular implementation of IP networking went off in its own direction.
4.2BSD introduced a function inet_aton(), …
[which] allowed octal and hexadecimal in addition to decimal,
distinguishing these radices by using the C language syntax
involving a prefix “0” or “0x”, and allowed the numbers to be arbitrarily long.
The 4.2BSD inet_aton() has been widely copied and imitated,
and so is a de facto standard
for the textual representation of IPv4 addresses.
Nevertheless, these alternative syntaxes have now fallen out of use …
[and] All the forms except for decimal octets are seen as non-standard
(despite being quite widely interoperable) and undesirable.
So, even though [POSIX defines the behavior of inet_addr][4]
to interpret leading zero as octal (and leading “0x” as hex),
it may be safest to avoid it.
P.S. [RFC 790][3] has been obsoleted by [RFC 1700][5],
which uses decimal numbers of one, two, or three digits,
without leading zeroes.
[3]: https://www.rfc-editor.org/rfc/rfc790 "the "Assigned Numbers" RFC"
[4]: http://pubs.opengroup.org/onlinepubs/9699919799/functions/inet_addr.html
[5]: https://www.rfc-editor.org/rfc/rfc1700
This is something I have been thinking while reading programming books and in computer science class at school where we learned how to convert decimal values into hexadecimal.
Can someone please tell me what are the advantages of using hexadecimal values and why we use them in programmnig?
Thank you.
In many cases (like e.g. bit masks) you need to use binary, but binary is hard to read because of its length. Since hexadecimal values can be much easier translated to/from binary than decimals, you could look at hex values as kind of shorthand notation for binary values.
It certainly depends on what you're doing.
It comes as an extension of base 2, which you probably are familiar with as essential to computing.
Check this out for a good discussion of
several applications...
https://softwareengineering.stackexchange.com/questions/170440/why-use-other-number-bases-when-programming/
The hexadecimal digit corresponds 1:1 to a given pattern of 4 bits. With experience, you can map them from memory. E.g. 0x8 = 1000, 0xF = 1111, correspondingly, 0x8F = 10001111.
This is a convenient shorthand where the bit patterns do matter, e.g. in bit maps or when working with i/o ports. To visualize the bit pattern for 169d is in comparison more difficult.
A byte consists of 8 binary digits and is the smallest piece of data that computers normally work with. All other variables a computer works with are constructed from bytes. For example; a single character can be stored in a single byte, and a 32bit integer consists of 4 bytes.
As bytes are so fundamental we want a way to write down their value as neatly and efficiently as possible. One option would be to use binary, but then we would need a lot of digits. This takes up a lot of space and can be confusing when many numbers are written in sequence:
200 201 202 == 11001000 11001001 11001010
Using hexadecimal notation, we can write every byte using just two digits:
200 == C8
Also, as 16 is a power of 2, it is easy to convert between hexadecimal and binary representations in your head. This is useful as sometimes we are only interested in a single bit within the byte. As a simple example, if the first digit of a hexadecimal representation is 0 we know that the first four binary digits are 0.
How does the 68000 internally represent instructions.
I've read that there are different types of instructions: single effective operation word format instructions, brief and full extension word format instructions. The single effective operation word instruction seems to represent the instruction and the lower 6 bits of this instruction the addressing mode and register. Does this addressing mode and register tell you if there follows a brief or full extension word format instruction, which on his turn represents the operands for the instruction. Do you know a better manual than the 68000 programming reference manual.
Thanks in advance
The actual internal representation is a combination of "microcode" and "nanocode". The 68000 has 544 17-bit microcode words which dispaches to 366 68-bit nanocode words.
While this may not be what you wanted to know, this link may provide some insights:
http://www.easy68k.com/paulrsm/doc/dpbm68k1.htm
right, on m68000 indexed modes uses the brief extension. In "Address Register Indirect with Index (8-Bit Displacement) Mode" (d8, An, Xn), the BEW is filled with D/A (if Xn is a data or address register), Xn (the register number), W/L (to threat Xn contents as 16 or 32bits), scale to 0 (see note), and the 8-bit displacement.
on other hand, other modes, like the 16bit displacement, "Address with displacement" (d16,An) , the extension is only a word with the displacement.
the note is: brief extension word - m68k doesn't support the 2bits for scale so is set to 0; scale on BEW using the scale bits, and full extensions are only suported m68020,40,-> cpus. http://etd.dtu.dk/thesis/264182/bac10_19.pdf
I don't know very well about RAM and HDD architecture, or how electronics deals with chunks of memory, but this always triggered my curiosity:
Why did we choose to stop at 8 bits for the smallest element in a computer value ?
My question may look very dumb, because the answer are obvious, but I'm not very sure...
Is it because 2^3 allows it to fit perfectly when addressing memory ?
Are electronics especially designed to store chunk of 8 bits ? If yes, why not use wider words ?
It is because it divides 32, 64 and 128, so that processor words can be be given several of those words ?
Is it just convenient to have 256 value for such a tiny space ?
What do you think ?
My question is a little too metaphysical, but I want to make sure it's just an historical reason and not a technological or mathematical reason.
For the anecdote, I was also thinking about the ASCII standard, in which most of the first characters are useless with stuff like UTF-8, I'm also trying to think about some tinier and faster character encoding...
Historically, bytes haven't always been 8-bit in size (for that matter, computers don't have to be binary either, but non-binary computing has seen much less action in practice). It is for this reason that IETF and ISO standards often use the term octet - they don't use byte because they don't want to assume it means 8-bits when it doesn't.
Indeed, when byte was coined it was defined as a 1-6 bit unit. Byte-sizes in use throughout history include 7, 9, 36 and machines with variable-sized bytes.
8 was a mixture of commercial success, it being a convenient enough number for the people thinking about it (which would have fed into each other) and no doubt other reasons I'm completely ignorant of.
The ASCII standard you mention assumes a 7-bit byte, and was based on earlier 6-bit communication standards.
Edit: It may be worth adding to this, as some are insisting that those saying bytes are always octets, are confusing bytes with words.
An octet is a name given to a unit of 8 bits (from the Latin for eight). If you are using a computer (or at a higher abstraction level, a programming language) where bytes are 8-bit, then this is easy to do, otherwise you need some conversion code (or coversion in hardware). The concept of octet comes up more in networking standards than in local computing, because in being architecture-neutral it allows for the creation of standards that can be used in communicating between machines with different byte sizes, hence its use in IETF and ISO standards (incidentally, ISO/IEC 10646 uses octet where the Unicode Standard uses byte for what is essentially - with some minor extra restrictions on the latter part - the same standard, though the Unicode Standard does detail that they mean octet by byte even though bytes may be different sizes on different machines). The concept of octet exists precisely because 8-bit bytes are common (hence the choice of using them as the basis of such standards) but not universal (hence the need for another word to avoid ambiguity).
Historically, a byte was the size used to store a character, a matter which in turn builds on practices, standards and de-facto standards which pre-date computers used for telex and other communication methods, starting perhaps with Baudot in 1870 (I don't know of any earlier, but am open to corrections).
This is reflected by the fact that in C and C++ the unit for storing a byte is called char whose size in bits is defined by CHAR_BIT in the standard limits.h header. Different machines would use 5,6,7,8,9 or more bits to define a character. These days of course we define characters as 21-bit and use different encodings to store them in 8-, 16- or 32-bit units, (and non-Unicode authorised ways like UTF-7 for other sizes) but historically that was the way it was.
In languages which aim to be more consistent across machines, rather than reflecting the machine architecture, byte tends to be fixed in the language, and these days this generally means it is defined in the language as 8-bit. Given the point in history when they were made, and that most machines now have 8-bit bytes, the distinction is largely moot, though it's not impossible to implement a compiler, run-time, etc. for such languages on machines with different sized bytes, just not as easy.
A word is the "natural" size for a given computer. This is less clearly defined, because it affects a few overlapping concerns that would generally coïncide, but might not. Most registers on a machine will be this size, but some might not. The largest address size would typically be a word, though this may not be the case (the Z80 had an 8-bit byte and a 1-byte word, but allowed some doubling of registers to give some 16-bit support including 16-bit addressing).
Again we see here a difference between C and C++ where int is defined in terms of word-size and long being defined to take advantage of a processor which has a "long word" concept should such exist, though possibly being identical in a given case to int. The minimum and maximum values are again in the limits.h header. (Indeed, as time has gone on, int may be defined as smaller than the natural word-size, as a combination of consistency with what is common elsewhere, reduction in memory usage for an array of ints, and probably other concerns I don't know of).
Java and .NET languages take the approach of defining int and long as fixed across all architecutres, and making dealing with the differences an issue for the runtime (particularly the JITter) to deal with. Notably though, even in .NET the size of a pointer (in unsafe code) will vary depending on architecture to be the underlying word size, rather than a language-imposed word size.
Hence, octet, byte and word are all very independent of each other, despite the relationship of octet == byte and word being a whole number of bytes (and a whole binary-round number like 2, 4, 8 etc.) being common today.
Not all bytes are 8 bits. Some are 7, some 9, some other values entirely. The reason 8 is important is that, in most modern computers, it is the standard number of bits in a byte. As Nikola mentioned, a bit is the actual smallest unit (a single binary value, true or false).
As Will mentioned, this article http://en.wikipedia.org/wiki/Byte describes the byte and its variable-sized history in some more detail.
The general reasoning behind why 8, 256, and other numbers are important is that they are powers of 2, and computers run using a base-2 (binary) system of switches.
ASCII encoding required 7 bits, and EBCDIC required 8 bits. Extended ASCII codes (such as ANSI character sets) used the 8th bit to expand the character set with graphics, accented characters and other symbols.Some architectures made use of proprietary encodings; a good example of this is the DEC PDP-10, which had a 36 bit machine word. Some operating sytems on this architecture used packed encodings that stored 6 characters in a machine word for various purposes such as file names.
By the 1970s, the success of the D.G. Nova and DEC PDP-11, which were 16 bit architectures and IBM mainframes with 32 bit machine words was pushing the industry towards an 8 bit character by default. The 8 bit microprocessors of the late 1970s were developed in this environment and this became a de facto standard, particularly as off-the shelf peripheral ships such as UARTs, ROM chips and FDC chips were being built as 8 bit devices.
By the latter part of the 1970s the industry settled on 8 bits as a de facto standard and architectures such as the PDP-8 with its 12 bit machine word became somewhat marginalised (although the PDP-8 ISA and derivatives still appear in embedded sytem products). 16 and 32 bit microprocessor designs such as the Intel 80x86 and MC68K families followed.
Since computers work with binary numbers, all powers of two are important.
8bit numbers are able to represent 256 (2^8) distinct values, enough for all characters of English and quite a few extra ones. That made the numbers 8 and 256 quite important.
The fact that many CPUs (used to and still do) process data in 8bit helped a lot.
Other important powers of two you might have heard about are 1024 (2^10=1k) and 65536 (2^16=65k).
Computers are build upon digital electronics, and digital electronics works with states. One fragment can have 2 states, 1 or 0 (if the voltage is above some level then it is 1, if not then it is zero). To represent that behavior binary system was introduced (well not introduced but widely accepted).
So we come to the bit. Bit is the smallest fragment in binary system. It can take only 2 states, 1 or 0, and it represents the atomic fragment of the whole system.
To make our lives easy the byte (8 bits) was introduced. To give u some analogy we don't express weight in grams, but that is the base measure of weight, but we use kilograms, because it is easier to use and to understand the use. One kilogram is the 1000 grams, and that can be expressed as 10 on the power of 3. So when we go back to the binary system and we use the same power we get 8 ( 2 on the power of 3 is 8). That was done because the use of only bits was overly complicated in every day computing.
That held on, so further in the future when we realized that 8 bytes was again too small and becoming complicated to use we added +1 on the power ( 2 on the power of 4 is 16), and then again 2^5 is 32, and so on and the 256 is just 2 on the power of 8.
So your answer is we follow the binary system because of architecture of computers, and we go up in the value of the power to represent get some values that we can simply handle every day, and that is how you got from a bit to an byte (8 bits) and so on!
(2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and so on) (2^x, x=1,2,3,4,5,6,7,8,9,10 and so on)
The important number here is binary 0 or 1. All your other questions are related to this.
Claude Shannon and George Boole did the fundamental work on what we now call information theory and Boolean arithmetic. In short, this is the basis of how a digital switch, with only the ability to represent 0 OFF and 1 ON can represent more complex information, such as numbers, logic and a jpg photo. Binary is the basis of computers as we know them currently, but other number base computers or analog computers are completely possible.
In human decimal arithmetic, the powers of ten have significance. 10, 100, 1000, 10,000 each seem important and useful. Once you have a computer based on binary, there are powers of 2, likewise, that become important. 2^8 = 256 is enough for an alphabet, punctuation and control characters. (More importantly, 2^7 is enough for an alphabet, punctuation and control characters and 2^8 is enough room for those ASCII characters and a check bit.)
We normally count in base 10, a single digit can have one of ten different values. Computer technology is based on switches (microscopic) which can be either on or off. If one of these represents a digit, that digit can be either 1 or 0. This is base 2.
It follows from there that computers work with numbers that are built up as a series of 2 value digits.
1 digit,2 values
2 digits, 4 values
3 digits, 8 values etc.
When processors are designed, they have to pick a size that the processor will be optimized to work with. To the CPU, this is considered a "word". Earlier CPUs were based on word sizes of fourbits and soon after 8 bits (1 byte). Today, CPUs are mostly designed to operate on 32 bit and 64 bit words. But really, the two state "switch" are why all computer numbers tend to be powers of 2.
I believe the main reason has to do with the original design of the IBM PC. The Intel 8080 CPU was the first precursor to the 8086 which would later be used in the IBM PC. It had 8-bit registers. Thus, a whole ecosystem of applications was developed around the 8-bit metaphor. In order to retain backward compatibility, Intel designed all subsequent architectures to retain 8-bit registers. Thus, the 8086 and all x86 CPUs after that kept their 8-bit registers for backwards compatibility, even though they added new 16-bit and 32-bit registers over the years.
The other reason I can think of is 8 bits is perfect for fitting a basic Latin character set. You cannot fit it into 4 bits, but you can in 8. Thus, you get the whole 256-value ASCII charset. It is also the smallest power of 2 for which you have enough bits into which you can fit a character set. Of course, these days most character sets are actually 16-bit wide (i.e. Unicode).
Charles Petzold wrote an interesting book called Code that covers exactly this question. See chapter 15, Bytes and Hex.
Quotes from that chapter:
Eight bit values are inputs to the
adders, latches and data selectors,
and also outputs from these units.
Eight-bit values are also defined by
switches and displayed by lightbulbs,
The data path in these circuits is
thus said to be 8 bits wide. But
why 8 bits? Why not 6 or 7 or 9 or
10?
... there's really no reason why
it had to be built that way. Eight
bits just seemed at the time to be a
convenient amount, a nice biteful of
bits, if you will.
...For a while, a byte meant simply
the number of bits in a particular
data path. But by the mid-1960s. in
connection with the development of
IBM's System/360 (their large complex
of business computers), the word came
to mean a group of 8 bits.
... One reason IBM gravitated toward
8-bit bytes was the ease in storing
numbers in a format known as BCD.
But as we'll see in the chapters ahead, quite by coincidence a byte is
ideal for storing text because most
written languages around the world
(with the exception of the ideographs
used in Chinese, Japanese and Korean)
can be represented with fewer than 256
characters.
Historical reasons, I suppose. 8 is a power of 2, 2^2 is 4 and 2^4 = 16 is far too little for most purposes, and 16 (the next power of two) bit hardware came much later.
But the main reason, I suspect, is the fact that they had 8 bit microprocessors, then 16 bit microprocessors, whose words could very well be represented as 2 octets, and so on. You know, historical cruft and backward compability etc.
Another, similarily pragmatic reason against "scaling down": If we'd, say, use 4 bits as one word, we would basically get only half the troughtput compared with 8 bit. Aside from overflowing much faster.
You can always squeeze e.g. 2 numbers in the range 0..15 in one octet... you just have to extract them by hand. But unless you have, like, gazillions of data sets to keep in memory side-by-side, this isn't worth the effort.
For a computer working with a 64 bit processor, the largest number that it can handle would be 264 = 18,446,744,073,709,551,616. How does programming languages, say Java or be it C, C++ handle arithmetic of numbers higher than this value. Any register cannot hold it as a single piece. How was this issue tackled?
There are lots of specialized techniques for doing calculations on numbers larger than the register size. Some of them are outlined in this wikipedia article on arbitrary precision arithmetic
Low level languages, like C and C++, leave large number calculations to the library of your choice. One notable one is the GNU Multi-Precision library. High level languages like Python, and others, integrate this into the core of the language, so normal numbers and very large numbers are identical to the programmer.
You assume the wrong thing. The biggest number it can handle in a single register is a 64-bits number. However, with some smart programming techniques, you could just combined a few dozens of those 64-bits numbers in a row to generate a huge 6400 bit number and use that to do more calculations. It's just not as fast as having the number fit in one register.
Even the old 8 and 16 bits processors used this trick, where they would just let the number overflow to other registers. It makes the math more complex but it doesn't put an end to the possibilities.
However, such high-precision math is extremely unusual. Even if you want to calculate the whole national debt of the USA and store the outcome in Zimbabwean Dollars, a 64-bits integer would still be big enough, I think. It's definitely big enough to contain the amount of my savings account, though.
Programming languages that handle truly massive numbers use custom number primitives that go beyond normal operations optimized for 32, 64, or 128 bit CPUs. These numbers are especially useful in computer security and mathematical research.
The GNU Multiple Precision Library is probably the most complete example of these approaches.
You can handle larger numbers by using arrays. Try this out in your web browser. Type the following code in the JavaScript console of your web browser:
The point at which JavaScript fails
console.log(9999999999999998 + 1)
// expected 9999999999999999
// actual 10000000000000000 oops!
JavaScript does not handle plain integers above 9999999999999998. But writing your own number primitive is to make this calculation work is simple enough. Here is an example using a custom number adder class in JavaScript.
Passing the test using a custom number class
// Require a custom number primative class
const {Num} = require('./bases')
// Create a massive number that JavaScript will not add to (correctly)
const num = new Num(9999999999999998, 10)
// Add to the massive number
num.add(1)
// The result is correct (where plain JavaScript Math would fail)
console.log(num.val) // 9999999999999999
How it Works
You can look in the code at class Num { ... } to see details of what is happening; but here is a basic outline of the logic in use:
Classes:
The Num class contains an array of single Digit classes.
The Digit class contains the value of a single digit, and the logic to handle the Carry flag
Steps:
The chosen number is turned into a string
Each digit is turned into a Digit class and stored in the Num class as an array of digits
When the Num is incremented, it gets carried to the first Digit in the array (the right-most number)
If the Digit value plus the Carry flag are equal to the Base, then the next Digit to the left is called to be incremented, and the current number is reset to 0
... Repeat all the way to the left-most digit of the array
Logistically it is very similar to what is happening at the machine level, but here it is unbounded. You can read more about about how digits are
carried here; this can be applied to numbers of any base.
Ada actually supports this natively, but only for its typeless constants ("named numbers"). For actual variables, you need to go find an arbitrary-length package. See Arbitrary length integer in Ada
More-or-less the same way that you do. In school, you memorized single-digit addition, multiplication, subtraction, and division. Then, you learned how to do multiple-digit problems as a sequence of single-digit problems.
If you wanted to, you could multiply two twenty-digit numbers together using nothing more than knowledge of a simple algorithm, and the single-digit times tables.
In general, the language itself doesn't handle high-precision, high-accuracy large number arithmetic. It's far more likely that a library is written that uses alternate numerical methods to perform the desired operations.
For example (I'm just making this up right now), such a library might emulate the actual techniques that you might use to perform that large number arithmetic by hand. Such libraries are generally much slower than using the built-in arithmetic, but occasionally the additional precision and accuracy is called for.
As a thought experiment, imagine the numbers stored as a string. With functions to add, multiply, etc these arbitrarily long numbers.
In reality these numbers are probably stored in a more space efficient manner.
Think of one machine-size number as a digit and apply the algorithm for multi-digit multiplication from primary school. Then you don't need to keep the whole numbers in registers, just the digits as they are worked on.
Most languages store them as array of integers. If you add/subtract two to of these big numbers the library adds/subtracts all integer elements in the array separately and handles the carries/borrows.
It's like manual addition/subtraction in school because this is how it works internally.
Some languages use real text strings instead of integer arrays which is less efficient but simpler to transform into text representation.