I come across the below statement while studying about HTML Character Sets and Character Encoding :
Since ASCII used 7 bits for the character, it could only represent 128
different characters.
When we convert any decimal value from the ASCII character set to its binary equivalent it comes down to a 7-bits long binary number.
E.g. For Capital English Letter 'E' the decimal value of 69 exists in ASCII table. If we convert '69' to it's binary equivalent it comes down to the 7-bits long binary number 1000101
Then, why in the ASCII Table it's been mentioned as a 8-bits long binary number 01000101 instead of a 7-bits long binary number 1000101 ?
This is contradictory to the statement
Since ASCII used 7 bits for the character, it could only represent 128
different characters.
The above statement is saying that ASCII used 7 bits for the character.
Please clear my confusion about considering the binary equivalent of a decimal value. Whether should I consider a 7-bits long binary equivalent or a 8-bits long binary equivalent of any decimal value from the ASCII Table? Please explain to me in an easy to understand language.
Again, consider the below statement :
Since ASCII used 7 bits for the character, it could only represent 128
different characters.
According to the above statement how does the number of characters(128) that ASCII supports relates to the fact that ASCII uses 7 bits to represent any character?
Please clear the confusion.
Thank You.
In most processors, memory is byte-addressable and not bit-addressable. That is, a memory address gives the location of an 8-bit value. So, almost all data is manipulated in multiples of 8 bits at a time.
If we were to store a value that has by its nature only 7 bits, we would very often use one byte per value. If the data is a sequence of such values, as text might be, we would still use one byte per value to make counting, sizing, indexing and iterating easier.
When we describe the value of a byte, we often show all of its bits, either in binary or hexadecimal. If a value is some sort of integer (say of 1, 2, 4, or 8 bytes) and its decimal representation would be more understandable, we would write the decimal digits for the whole integer. But in those cases, we might lose the concept of how many bytes it is.
BTW—HTML doesn't have anything to do with ASCII. And, Extended ASCII isn't one encoding. The fundamental rule of character encodings is to read (decode) with the encoding the text was written (encoded) with. So, a communication consists of the transferring of bytes and a shared understanding of the character encoding. (That makes saying "Extended ASCII" so inadequate as to be nearly useless.)
An HTML document represents a sequence of Unicode characters. So, one of the Unicode character encodings (UTF-8) is the most common encoding for an HTML document. Regardless, after it is read, the result is Unicode. An HTML document could be encoded in ASCII but, why do that? If you did know it was ASCII, you could just as easily know that it's UTF-8.
Outside of HTML, ASCII is used billions—if not trillions—of times per second. But, unless you know exactly how it pertains to your work, forget about it, you probably aren't using ASCII.
I've always wondered why leading zeroes (0) are used to represent octal numbers, instead of — for example — 0o. The use of 0o would be just as helpful, but would not cause as many problems as leading 0es (e.g. parseInt('08'); in JavaScript). What are the reason(s) behind this design choice?
All modern languages import this convention from C, which imported it from B, which imported it from BCPL.
Except BCPL used #1234 for octal and #x1234 for hexadecimal. B has departed from this convention because # was an unary operator in B (integer to floating point conversion), so #1234 could not be used, and # as a base indicator was replaced with 0.
The designers of B tried to make the syntax very compact. I guess this is the reason they did not use a two-character prefix.
Worth noting that in Python 3.0, they decided that octal literals must be prefixed with '0o' and the old '0' prefix became a SyntaxError, for the exact reasons you mention in your question
https://www.python.org/dev/peps/pep-3127/#removal-of-old-octal-syntax
"0b" is often used for binary rather than for octal. The leading "0" is, I suspect for "O -ctal".
If you know you are going to be parsing octal then use parseInt('08', 10); to make it treat the number as base ten.
I have a homework question regarding operator precedence in Fortran. In order to understand the question I need to know how to use binary numbers in Fortran. Can someone give me an example of how to use binary numbers in fortran? (Specifically with subtraction).
You need to be a bit clearer about what you mean by 'binary numbers in fortran'. In one sense, not terribly useful, all Fortran numbers are binary, as indeed most numbers in most programming languages are binary once they get onto the computer.
Fortran, in the standard at least, does not have the concept of a binary intrinsic data type, it has integers, reals, complex numbers, logicals and characters. Of course, your compiler might implement other types as well, but you don't tell us what that compiler is.
Standard Fortran does have the concept of binary input and output formats -- look for the 'B edit descriptor' in your documentation. This can be used on input and output to read and write binary representations of integers. But the numbers are, to Fortran, integers. So, if you were to read a, b as binary numbers, you would subtract them with the statement a-b.
Fortran does have a set of bit intrinsic procedures, which go by the names iand, ibclr, ieor and so forth but these are really for bit-twiddling.
If you can clarify your questions, I, or some other SOer, might be able to clarify an answer.
Finally, I think it's rather odd that you think you need to know about Fortran 'binary' numbers in order to understand operator precedence. Perhaps you could explain a bit more.
I was looking at this question. Basically having a leading zero causes the number to be interpreted as octal. I've ran into this problem numerous times in multiple languages.
Why doesn't the language explicitly require you to specify octal with a function call or a type (in strong typed languages) like:
oct variable = 2;
I can understand why hexadecimal (0x0234) has this format. Hex is pretty useful. An integer from the database will never have an x in it.
But octal numbers 0123 look like ints and are a pain to deal with. I've never used octal for anything.
Can anyone explain the rationale behind this usage? Is it just a bit of historical cruft?
It's largely historic. The best solution I've seen is in the new version of Python, where octal is indicated with a special prefix character "o", much like hexadecimal's "x" prefix:
0o10 == 0x8 == 8
99.9% of the reason it exists is to support chmod() calls, i.e. chmod(fd, 0755).
It does rather seem like a format more like hex's would be superior.
It exists since working with 3-bit segments is almost as useful as working with 4-bit segments. This was more true in the past (e.g., seven-segment LEDs, chmod, etc.).
The real question is why haven't more languages adopted octal and binary notations in a more regular fashion:
10 == 0b1010 == 0o12 == 0x0A
I know that Python finally adopted the 0o8 notation... not sure if they have adopted the binary one as well. I guess a better question is Why does this still trip people up?
I hate this too, I don't know why it's been carried forward into so many modern languages. I once knew someone who had a zip code like "09827" when he lived in NYC. Sometimes he had to input his zip code as "9827," because the leading zero would lead to error messages (since 9's and 8's are illegal characters in octal numbers).
Yes, it's historical. C uses this way to specify literals in octal, and possibly it was used somewhere before that.
I've experienced it in Javascript, where parsing dates stops working in august. Up to july it works as '07' parsed as octal is still seven, but '08' is not a valid number... (The solution is to specify the number base in the parseInt call.)
In C# there are no binary or octal literals, perhaps the reasoning is that you shouldn't do as much bit fiddling that the language needs it...
Personally, I blame the programmer in this case. Why are you formatting an integer by zero padding? Zero padding is for strings, not numeric types.
Why do most computer programming languages not allow binary numbers to be used like decimal or hexadecimal?
In VB.NET you could write a hexadecimal number like &H4
In C you could write a hexadecimal number like 0x04
Why not allow binary numbers?
&B010101
0y1010
Bonus Points!... What languages do allow binary numbers?
Edit
Wow! - So the majority think it's because of brevity and poor old "waves" thinks it's due to the technical aspects of the binary representation.
Because hexadecimal (and rarely octal) literals are more compact and people using them usually can convert between hexadecimal and binary faster than deciphering a binary number.
Python 2.6+ allows binary literals, and so do Ruby and Java 7, where you can use the underscore to make byte boundaries obvious. For example, the hexadedecimal value 0x1b2a can now be written as 0b00011011_00101010.
In C++0x with user defined literals binary numbers will be supported, I'm not sure if it will be part of the standard but at the worst you'll be able to enable it yourself
int operator "" _B(int i);
assert( 1010_B == 10);
In order for a bit representation to be meaningful, you need to know how to interpret it.
You would need to specify what the type of binary number you're using (signed/unsigned, twos-compliment, ones-compliment, signed-magnitude).
The only languages I've ever used that properly support binary numbers are hardware description languages (Verilog, VHDL, and the like). They all have strict (and often confusing) definitions of how numbers entered in binary are treated.
See perldoc perlnumber:
NAME
perlnumber - semantics of numbers and numeric operations in Perl
SYNOPSIS
$n = 1234; # decimal integer
$n = 0b1110011; # binary integer
$n = 01234; # octal integer
$n = 0x1234; # hexadecimal integer
$n = 12.34e-56; # exponential notation
$n = "-12.34e56"; # number specified as a string
$n = "1234"; # number specified as a string
Slightly off-topic, but newer versions of GCC added a C extension that allows binary literals. So if you only ever compile with GCC, you can use them. Documenation is here.
Common Lisp allows binary numbers, using #b... (bits going from highest-to-lowest power of 2). Most of the time, it's at least as convenient to use hexadecimal numbers, though (by using #x...), as it's fairly easy to convert between hexadecimal and binary numbers in your head.
Hex and octal are just shorter ways to write binary. Would you really want a 64-character long constant defined in your code?
Common wisdom holds that long strings of binary digits, eg 32 bits for an int, are too difficult for people to conveniently parse and manipulate. Hex is generally considered easier, though I've not used either enough to have developed a preference.
Ruby which, as already mentioned, attempts to resolve this by allowing _ to be liberally inserted in the literal , allowing, for example:
irb(main):005:0> 1111_0111_1111_1111_0011_1100
=> 111101111111111100111100
D supports binary literals using the syntax 0[bB][01]+, e.g. 0b1001. It also allows embedded _ characters in numeric literals to allow them to be read more easily.
Java 7 now has support for binary literals. So you can simply write 0b110101. There is not much documentation on this feature. The only reference I could find is here.
While C only have native support for 8, 10 or 16 as base, it is actually not that hard to write a pre-processor macro that makes writing 8 bit binary numbers quite simple and readable:
#define BIN(d7,d6,d5,d4, d3,d2,d1,d0) \
( \
((d7)<<7) + ((d6)<<6) + ((d5)<<5) + ((d4)<<4) + \
((d3)<<3) + ((d2)<<2) + ((d1)<<1) + ((d0)<<0) \
)
int my_mask = BIN(1,1,1,0, 0,0,0,0);
This can also be used for C++.
for the record, and to answer this:
Bonus Points!... What languages do allow binary numbers?
Specman (aka e) allows binary numbers. Though to be honest, it's not quite a general purpose language.
Every language should support binary literals. I go nuts not having them!
Bonus Points!... What languages do allow binary numbers?
Icon allows literals in any base from 2 to 16, and possibly up to 36 (my memory grows dim).
It seems the from a readability and usability standpoint, the hex representation is a better way of defining binary numbers. The fact that they don't add it is probably more of user need that a technology limitation.
I expect that the language designers just didn't see enough of a need to add binary numbers. The average coder can parse hex just as well as binary when handling flags or bit masks. It's great that some languages support binary as a representation, but I think on average it would be little used. Although binary -- if available in C, C++, Java, C#, would probably be used more than octal!
In Smalltalk it's like 2r1010. You can use any base up to 36 or so.
Hex is just less verbose, and can express anything a binary number can.
Ruby has nice support for binary numbers, if you really want it. 0b11011, etc.
In Pop-11 you can use a prefix made of number (2 to 32) + colon to indicate the base, e.g.
2:11111111 = 255
3:11111111 = 3280
16:11111111 = 286331153
31:11111111 = 28429701248
32:11111111 = 35468117025
Forth has always allowed numbers of any base to be used (up to size limit of the CPU of course). Want to use binary: 2 BASE ! octal: 8 BASE ! etc. Want to work with time? 60 BASE ! These examples are all entered from base set to 10 decimal. To change base you must represent the base desired from the current number base. If in binary and you want to switch back to decimal then 1010 BASE ! will work. Most Forth implementations have 'words' to shift to common bases, e.g. DECIMAL, HEX, OCTAL, and BINARY.
Although it's not direct, most languages can also parse a string. Java can convert "10101000" into an int with a method.
Not that this is efficient or anything... Just saying it's there. If it were done in a static initialization block, it might even be done at compile time depending on the compiler.
If you're any good at binary, even with a short number it's pretty straight forward to see 0x3c as 4 ones followed by 2 zeros, whereas even that short a number in binary would be 0b111100 which might make your eyes hurt before you were certain of the number of ones.
0xff9f is exactly 4+4+1 ones, 2 zeros and 5 ones (on sight the bitmask is obvious). Trying to count out 0b1111111110011111 is much more irritating.
I think the issue may be that language designers are always heavily invested in hex/octal/binary/whatever and just think this way. If you are less experienced, I can totally see how these conversions wouldn't be as obvious.
Hey, that reminds me of something I came up with while thinking about base conversions. A sequence--I didn't think anyone could figure out the "Next Number", but one guy actually did, so it is solvable. Give it a try:
10
11
12
13
14
15
16
21
23
31
111
?
Edit:
By the way, this sequence can be created by feeding sequential numbers into single built-in function in most languages (Java for sure).