Is there a name for or common way to describe numbers where in binary only one bit would be set?
00000001 1
00000010 2
00000100 4
00001000 8
...
You could call them powers of two.
Powers of Two: http://en.wikipedia.org/wiki/Powers_of_two
Flags or bit fields http://en.wikipedia.org/wiki/Bit_field
Related
I'm doing like (-57)8 + (-76)8 then finding the 8's complement of -76 which i got 2 , and adding that to -57 which in turn gives -55 which is wrong, the answer should be -155. How to get that?
"then finding the 8's complement of -76 which i got 2" implies a 2 digit 8's complement. (-57)8 + (-76)8 overflows a 2 digit 8's complement encoding.
Use a wider 8's complement, like 4 digits.
I am trying to represent the maximum 64-bit unsigned value in different bases.
For base 2 (binary) it would be 64 1's:
1111111111111111111111111111111111111111111111111111111111111111
For base 16 (hex) it would be 16 F's
FFFFFFFFFFFFFFFF
For base 10 (decimal) it would be:
18446744073709551615
I'm trying to get the representation of this value in base 36 (it uses 0-9 and A-Z). There are many online base converters, but they all fail to produce the correct representation because they are limited by 64-bit math.
Does anyone know how to use DC (which is an extremely hard to use string math processors that can handle numbers of unlimited magnitude) and know how to do this conversion? Either that or can anyone tell me how I can perform this conversion with a calculator that won't fail due to integer roll-over?
I mad a quick test with ruby:
i = 'FFFFFFFFFFFFFFFF'.to_i(16)
puts i #18446744073709551615
puts i.to_s(36) #3w5e11264sgsf
You may also use larger numbers:
i = 'FFFFFFFFFFFFFFFF'.to_i(16) ** 16
puts i
puts i.to_s(36)
result:
179769313486231590617005494896502488139538923424507473845653439431848569886227202866765261632299351819569917639009010788373365912036255753178371299382143631760131695224907130882552454362167933328609537509415576609030163673758148226168953269623548572115351901405836315903312675793605327103910016259918212890625
1a1e4vngailcqaj6ud31s2kk9s94o3tyofvllrg4rx6mxa0pt2sc06ngjzleciz7lzgdt55aedc9x92w0w2gclhijdmj7le6osfi1w9gvybbfq04b6fm705brjo535po1axacun6f7013c4944wa7j0yyg93uzeknjphiegfat0ojki1g5pt5se1ylx93knpzbedn29
A short explanation what happens with big numbers:
Normal numbers are Fixnums. If you get larger numbers, the number becomes a Bignum:
small = 'FFFFFFF'.to_i(16)
big = 'FFFFFFFFFFFFFFFF'.to_i(16) ** 16
puts "%i is a %s" % [ small, small.class ]
puts "%i\n is a %s" % [ big, big.class ]
puts "%i^2 is a %s" % [ small, (small ** 2).class ]
Result:
268435455 is a Fixnum
179769313486231590617005494896502488139538923424507473845653439431848569886227202866765261632299351819569917639009010788373365912036255753178371299382143631760131695224907130882552454362167933328609537509415576609030163673758148226168953269623548572115351901405836315903312675793605327103910016259918212890625
is a Bignum
268435455^2 is a Bignum
From the documentation of Bignum:
Bignum objects hold integers outside the range of Fixnum. Bignum objects are created automatically when integer calculations would otherwise overflow a Fixnum. When a calculation involving Bignum objects returns a result that will fit in a Fixnum, the result is automatically converted.
It can be done with dc, but the output is not extremely useful.
$ dc
36
o
16
i
FFFFFFFFFFFFFFFF
p
03 32 05 14 01 01 02 06 04 28 16 28 15
Here's the explanation:
Entering a number by itself pushes that number
o pops the stack and sets the output radix.
i pops the stack and sets the input radix.
p prints the top number on the stack, in the current output radix. However, dc prints any output with a higher radix than 16 as binary (not ASCII).
In dc, the commands may be all put on the same line, like so:
$ dc
36o16iFFFFFFFFFFFFFFFFp
03 32 05 14 01 01 02 06 04 28 16 28 15
Get any language that can handle arbitrarily large integers. Ruby, Python, Haskell, you name it.
Implement the basic step: modulo 36 gives you the next digit, division by 36 gives you the number with the last digit cut out.
Map the digits to characters the way you like. For instance, '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'[digit] is fine by me. Append digits to the result as you produce them.
???
Return the concatenated string of digits. Profit!
Why do we have Base64 encoding? I am a beginner and I really don't understand why would you obfuscate the bytes into something else (unless it is encryption). In one of the books I read Base64 encoding is useful when binary transmission is not possible. Eg. When we post a form it is encoded. But why do we convert bytes into letters? Couldn't we just convert bytes into string format with a space in between? For example, 00000001 00000004? Or simply 0000000100000004 without any space because bytes always come in pair of 8?
Base64 is a way to encode binary data into an ASCII character set known to pretty much every computer system, in order to transmit the data without loss or modification of the contents itself.
For example, mail systems cannot deal with binary data because they expect ASCII (textual) data. So if you want to transfer an image or another file, it will get corrupted because of the way it deals with the data.
Note: base64 encoding is NOT a way of encrypting, nor a way of compacting data. In fact a base64 encoded piece of data is 1.333… times bigger than the original datapiece. It is only a way to be sure that no data is lost or modified during the transfer.
Base64 is a mechanism to enable representing and transferring binary data over mediums that allow only printable characters.It is most popular form of the “Base Encoding”, the others known in use being Base16 and Base32.
The need for Base64 arose from the need to attach binary content to emails like images, videos or arbitrary binary content . Since SMTP [RFC 5321] only allowed 7-bit US-ASCII characters within the messages, there was a need to represent these binary octet streams using the seven bit ASCII characters...
Hope this answers the Question
Base64 is a more or less compact way of transmitting (encoding, in fact, but with goal of transmitting) any kind of binary data.
See http://en.wikipedia.org/wiki/Base64
"The general rule is to choose a set of 64 characters that is both part of a subset common to most encodings, and also printable."
That's a very general purpose and the common need is not to waste more space than needed.
Historically, it's based on the fact that there is a common subset of (almost) all encodings used to store chars into bytes and that a lot of the 2^8 possible bytes risk loss or transformations during simple data transfer (for example a copy-paste-emailsend-emailreceive-copy-paste sequence).
(please redirect upvote to Brian's comment, I just make it more complete and hopefully more clear).
For data transmission, data can be textual or non-text(binary) like image, video, file etc.
As we know, during transmission only a stream of data(textual/printable characters) can be sent or received, hence we need a way encode non-text data like image, video, file.
Binary and ASCII representation of non-text(image, video, file) is easily obtainable.
Such non-text(binary) represenation is encoded in textual format such that each ASCII character takes one out of sixty four(A-Z, a-z, 0-9, + and /) possible character set.
Table 1: The Base 64 Alphabet
Value Encoding Value Encoding Value Encoding Value Encoding
0 A 17 R 34 i 51 z
1 B 18 S 35 j 52 0
2 C 19 T 36 k 53 1
3 D 20 U 37 l 54 2
4 E 21 V 38 m 55 3
5 F 22 W 39 n 56 4
6 G 23 X 40 o 57 5
7 H 24 Y 41 p 58 6
8 I 25 Z 42 q 59 7
9 J 26 a 43 r 60 8
10 K 27 b 44 s 61 9
11 L 28 c 45 t 62 +
12 M 29 d 46 u 63 /
13 N 30 e 47 v
14 O 31 f 48 w (pad) =
15 P 32 g 49 x
16 Q 33 h 50 y
These sixty four character set is called Base64 and encoding a given data into this character set having sixty four allowed characters is called Base64 encoding.
Let us take examples of few ASCII characters when encoded to Base64.
1 ==> MQ==
12 ==> MTI=
123 ==> MTIz
1234 ==> MTIzNA==
12345 ==> MTIzNDU=
123456 ==> MTIzNDU2
Here few points are to be noted:
Base64 encoding occurs in size of 4 characters. Because an ASCII character can take any out of 256 characters, which needs 4 characters of Base64 to cover. If the given ASCII value is represented in lesser character then rest of characters are padded with =.
= is not part of base64 character set. It is used for just padding.
Hence, one can see that the Base64 encoding is not encryption but just a way to transform any given data into a stream of printable characters which can be transmitted over network.
I had always been taught 0–9 to represent values zero to nine, and A, B, C, D, E, F for 10-15.
I see this format 0x00000000 and it doesn't fit into the pattern of hexadecimal. Is there a guide or a tutor somewhere that can explain it?
I googled for hexadecimal but I can't find any explanation of it.
So my 2nd question is, is there a name for the 0x00000000 format?
0x simply tells you the number after it will be in hex
so 0x00 is 0, 0x10 is 16, 0x11 is 17 etc
The 0x is just a prefix (used in C and many other programming languages) to mean that the following number is in base 16.
Other notations that have been used for hex include:
$ABCD
ABCDh
X'ABCD'
"ABCD"X
Yes, it is hexadecimal.
Otherwise, you can't represent A, for example. The compiler for C and Java will treat it as variable identifier. The added prefix 0x tells the compiler it's hexadecimal number, so:
int ten_i = 10;
int ten_h = 0xA;
ten_i == ten_h; // this boolean expression is true
The leading zeroes indicate the size: 0x0080 hints the number will be stored in two bytes; and 0x00000080 represents four bytes. Such notation is often used for flags: if a certain bit is set, that feature is enabled.
P.S. As an off-topic note: if the number starts with 0, then it's interpreted as octal number, for example 010 == 8. Here 0 is also a prefix.
Everything after the x are hex digits (the 0x is just a prefix to designate hex), representing 32 bits (if you were to put 0xFFFFFFFF in binary, it would be 1111 1111 1111 1111 1111 1111 1111 1111).
hexadecimal digits are often prefaced with 0x to indicate they are hexadecimal digits.
In this case, there are 8 digits, each representing 4 bits, so that is 32 bits or a word. I"m guessing you saw this in an error, and it is a memory address. this value means null, as the hex value is 0.
I'm working with a binary protocol that uses LLV to encode some variables.
I was given an example below which is used to specify a set of 5 chars to display.
F1 F0 F5 4C 69 6E 65 31
the F1 is specific to my device, it indicates display text on line one. The f0 and f5 I'm not sure about, the rest looks like ASCII text.
Anyone know how this encoding works exactly?
LLV is referenced in this protocol spec. pasted below, but doesn't seem to be defined in there.
http://www.google.com/url?sa=t&source=web&cd=1&ved=0CBIQFjAA&url=http%3A%2F%2Fwww.terminalhersteller.de%2FDownload%2FPA00P016_03_en.pdf&ei=yUFPTOSzH432tgON5PjuBw&usg=AFQjCNGjS_y264qKIRCSJQpdhlSXWtiadw&sig2=jMGtIwd42dozDSq7ub844w
Since the F1 is device-specific, this leaves the rest as F0 F5 ..., and this looks like an LLVAR sequence, in which the first two bytes specify the length of the rest (decimal 05 here). My guess would be that the whole data represents F1 "Line1", which looks quite reasonable.
By the way, LLVAR stands for "VARiable length with two decimal digits specifying the length". With three decimal digits for the length, it's LLLVAR.