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Int to Byte conversion not representing in hexadecimal in Python

I'm having some difficulty in understanding how python converts between int and byte data types and specifically why it isn't consistent with representing it as hexadecimal numbers.
Consider the following where I convert the number 13 into a 2 byte representation:
>>> (13).to_bytes(2, byteorder='big')
b'\x00\r'
Why does it use the character r in the second byte location?
In this case I would have expected it to output:
b'\x00\xD'
Doing the reverse in both cases outputs the correct answer.
>>> int.from_bytes(b'\x00\x0D', byteorder='big')
13
>>> int.from_bytes(b'\x00\r', byteorder='big')
13
And both have the correct number of bytes
>>> len(b'\x00\x0D')
2
>>> len(b'\x00\r')
2

There is a difference between bytes and a hexadecimal representation. bytes is a datatype; hexadecimal is a way of representing bit patterns on the screen.
A bytes is an immutable sequence of 8-bit values. The interpreter displays it, where possible, as characters or as string escape sequences, and where not possible, in hexadecimal. The corresponding literal is called a bytestring. In other words, hexadecimal is a sort of last resort. You can construct the bytes b'ABC' using hexadecimal notation: b'\x41\x42\x43' but the interpreter will still report it as b'ABC'. That is no different from the way quotes are handled:
>>> a = "ABC"
>>> a
'ABC'
>>> a = 'AB\'C'
>>> a
"AB'C"
The interpreter has a standard way of displaying its data and takes no account of the way you entered that data in the first place. This isn't a roundtrip failure, because no information is lost. You are seeing an equivalent representation rather than the same representation, is all.
If you want to see a hexadecimal representation then you should ask for it explicitly, instead of relying on the interpreter's default way of displaying a particular datatype.
>>> fmt = '\\x{0:02X}\\x{1:02X}'
>>> print(fmt.format(*((13).to_bytes(2, byteorder='big'))))
\x00\0D

There are some special escape sequences which are so common that they are not explicitly represented with their hex values:
\a <-> \x07 alert
\b <-> \x08 backspace
\t <-> \x09 tab (horizontal)
\n <-> \x0A new line
\v <-> \x0B vertical tab
\f <-> \x0C formfeed
\r <-> \x0D carriage return
\" <-> \x22 "
\' <-> \x27 '
\\ <-> \x5C \
you find a full list of escape sequences and how they work here.
Note that there is also \0 <-> \x00 in the C language.

python write file dealing with encode

I'm confused. I need HELP!!!
I'm dealing with a file contains Chinese characters,for instance, let's call it a.TEST, and here is what's inside.
你好 中国 Hello China 1 2 3
You don't need to understand what the chinese means.(Actually it's 'hello China')
>>> f=open('wr.TRAIN')
>>> print f.read()
你好 中国 Hello China 1 2 3
>>> f.seek(0)
>>> content = f.readline()
>>> content
'\xe4\xbd\xa0\xe5\xa5\xbd \xe4\xb8\xad\xe5\x9b\xbd Hello China 1 2 3\n'
>>> print content
你好 中国 Hello China 1 2 3
>>> type(content)
<type 'str'>
>>> isinstance(content,unicode)
False
Here comes the first Question: Why python shell give me the utf-8of content when i just type content,meanwhile print content cmd can output the form that I want to see?
The Second Question: what's the difference between unicode and str?
Someone told me that encode is convert unicode to str, but what i learned from Unicode HowTo tells me encode is convert unicode to utf-8
Not over yet! :)
here is test.py
#!/usr/bin/python
#-*- coding: utf-8 -*-
fr = open('a.TEST')
fw = open('out.TEST','w')
content = fr.readline()
content_list = content.split()
print content
fw.write('{0}'.format(content_list))
fr.close()
fw.close()
Third Question:Why the chinese character turn into utf-8 code when I do .split()?
and I thought fw.write('{0}'.format(content_list).decode('utf-8')) will work, but it doesn't.
I don't want what's written into out.TEST is character encoding form, I want it to be exactly the character that look like originally（你好）. How to do it?

What is Encoding
A file consists of bytes. You can represent each byte with a number between 0 and 255 (or 0x00 and 0xFF in hexadecimal).
Text is also written as bytes. There is an agreement on the way text is written. That is an encoding. The most basic encoding is ASCII and other encodings are usually based on it. For example, ASCII defines that number 65 (0x41) represents 'A', 66 (0x42) represents 'B' etc.
How are Strings Represented
In python, you can define a string using numeric values:
>>> '\x41\x42\x43'
'ABC'
'\x41\x42\x43' is exactly the same thing as 'ABC'. Python will always represent the string using the more readable textual representation ('ABC').
However, some numeric values are not printable characters, so they will be represented in numeric form:
>>> '\x00\x01\x02\x03\x04'
'\x00\x01\x02\x03\x04'
Others characters have aliases to make your job easier:
>>> '\x0a\x0d\x09'
'\n\r\t'
Different Encodings
ASCII table defines meaning of numbers 0-127 and includes only the english alphabet. Numbers 128-255 are undefined. So, other encodings define a meaning for 128-255. Yet others change the meaning of the whole range 0-255.
There are many encodings and they define 128-255 differently.
For example, character 185 (0xB9) is ą in windows-1250 encoding, but it is š in iso-8859-2 encoding.
So, what happens if you print \xb9? It depends on the encoding used in the console. In my case (my console uses cp852 encoding) it is:
>>> print '\xb9'
╣
Because of that ambiguity, string '\xb9' will never be represented as '╣' (nor 'ą'...). That would hide the true value. It will be represented as the numeric value:
>>> '\xb9'
'\xb9'
Also:
>>> '╣'
'\xb9'
See also the string from the question in my console:
>>> content = '\xe4\xbd\xa0\xe5\xa5\xbd \xe4\xb8\xad\xe5\x9b\xbd Hello China 1 2 3\n'
>>>
>>> content
'\xe4\xbd\xa0\xe5\xa5\xbd \xe4\xb8\xad\xe5\x9b\xbd Hello China 1 2 3\n'
>>>
>>> print content
ńŻáňąŻ ńŞşňŤŻ Hello China 1 2 3
But what happens if variable is just entered in the console?
When a variable is enteren in cosole without print, its representation is printed. It is the same as the following:
>>> print repr(content)
'\xe4\xbd\xa0\xe5\xa5\xbd \xe4\xb8\xad\xe5\x9b\xbd Hello China 1 2 3\n'
What is Unicode?
Unicode table aims to define a numeric representation of all characters in the world and more. It can actually do that, because it is not limited to 256 values (or to any other limit actually). This is not an encoding, but a universal mapping of numbers to characters.
For example, unicode defines that number 353 (0x0161) is character š. That is allways true regardless of your locale and encodings you use. That character can be stored in files (or memory) in any encoding which supports š.
What is UTF-8?
When encoding a unicode character, one can use any encoding, but not all of them will support all characters.
For example, š (unicode 0x0161) can be encoded in iso-8869-2 as 0xB9, but it cannot be encoded in iso-8869-1 at all.
So, to be able to encode anything, you need an encoding which supports every unicode character. UTF-8 is one of those encodings, but there are others:
>>> u'\u0161'.encode('utf-7')
'+AWE-'
>>> u'\u0161'.encode('utf-8')
'\xc5\xa1'
>>> u'\u0161'.encode('utf-16le')
'a\x01'
>>> u'\u0161'.encode('utf-16be')
'\x01a'
>>> u'\u0161'.encode('utf-32le')
'a\x01\x00\x00'
>>> u'\u0161'.encode('utf-32be')
'\x00\x00\x01a'
The good thing about utf-8 is that the whole ASCII range is unchanged and as long as only ASCII is used, only one byte is used per character:
>>> u'abcdefg'.encode('utf-8')
'abcdefg'
Unicode in Python 2
Important: This is really specific to Python 2. Python 3 is different.
Unlike str objects, which are strings of bytes, unicode objects are strings of unicode characters.
They can be encoded into a str in chosen encoding, or decoded from str in chosen encoding.
A unicode string is specified using u before the opening quote. The characters inside are interpreted using current encoding, or they can be specified in numeric format \uHEX:
>>> u'ABCD'
u'ABCD'
>>>
>>> u'\u0041\u0042\u0043'
u'ABC'
>>> u'šâů'
u'\u0161\xe2\u016f'
And Now the Answers
First Question
contents prints repr(contents)
print contents prints contents
Second Question
UTF-8 strings are byte strings (str). You get them by encoding the unicode:
>>> u'\u0161'.encode('utf-8')
'\xc5\xa1'
>>> '\xc5\xa1'.decode('utf-8')
u'\u0161'
So yes, encode converts unicode to str. The str can be utf-8, but it does not have to be.
Third Question
A) "Why the chinese character turn into utf-8 code when I do .split()?"
They were utf-8 all the time.
B) "I thought fw.write('{0}'.format(content_list).decode('utf-8')) will work"
content_list is not a string. It is a list. When a list is converted to a string, it is done using its repr, which also does repr of all of the contents.
For example:
>>> 'a \n a \n a'
'a \n a \n a'
>>> print 'a \n a \n a'
a
a
a
>>> print ['a \n a \n a']
['a \n a \n a']
The last print printed repr(list) which contains repr(str).

In the beginning, there was just english characters, and people was not satisfied.
Then they want to display every character in the world.But there is problem. One byte can only represent 255 characters. There just simply not enough place to hold them.
Then people decide to use two byte to represent one character.And call it 'utf8'.
No matter what characters you write in, it's all store in byte form.
In Python, there is no such datatype called 'unicode', just 'str'. And 'unicode' is an encoding system of 'str'.
'\xe4\xbd\xa0\xe5\xa5\xbd \xe4\xb8\xad\xe5\x9b\xbd' is byte form of "你好 中国".
It can not display without an encoding system specified.
I suppose you could blame linux/unix. Python has no problem to display 'utf-8' characters, while 'cat' cannot.

encoding unicode using UTF-8

In Python, if I type
euro = u'\u20AC'
euroUTF8 = euro.encode('utf-8')
print(euroUTF8, type(euroUTF8), len(euroUTF8))
the output is
('\xe2\x82\xac', <type 'str'>, 3)
I have two questions:
1. it looks like euroUTF8 is encoded over 3 bytes, but how do I get its binary representation to see how many bits it contain?
2. what does 'x' in '\xe2\x82\xac' mean? I don't think 'x' is a hex number. And why there are three '\'?

In Python 2, print is a statement, not a function. You are printing a tuple here. Print the individual elements by removing the (..):
>>> euro = u'\u20AC'
>>> euroUTF8 = euro.encode('utf-8')
>>> print euroUTF8, type(euroUTF8), len(euroUTF8)
€ <type 'str'> 3
Now you get the 3 individual objects written as strings to stdout; my terminal just happens to be configured to interpret anything written to it as UTF-8, so the bytes correctly result in the € Euro symbol being displayed.
The \x<hh> sequences are Python string literal escape sequences (see the reference documentation); they are the default output for the repr() applied to a string with non-ASCII, non-printable bytes in them. You'll see the same thing when echoing the value in an interactive interpreter:
>>> euroUTF8
'\xe2\x82\xac'
>>> euroUTF8[0]
'\xe2'
>>> euroUTF8[1]
'\x82'
>>> euroUTF8[2]
'\xac'
They provide you with ASCII-safe debugging output. The contents of all Python standard library containers use this format; including lists, tuples and dictionaries.
If you want to format to see the bits that make up these values, convert each byte to an integer by using the ord() function, then format the integer as binary:
>>> ' '.join([format(ord(b), '08b') for b in euroUTF8])
'11100010 10000010 10101100'

Each letter in each encoding are represented using different number of bits. UTF-8 is a 8 bit encoding, so there is no need to get a binary representation to know each bit count of each character. (If you still want to present bits, refer to Martijn's answer.)
\x means that the following value is a byte. So x is not something like a hex number that you should convert or read. It identifies the following value, which is you are interested in. \'s are used to escape that x's because they are not a part of the value.

How can I slice a substring from a unicode string with Python?

I have a unicode string as a result : u'splunk>\xae\uf001'
How can I get the substring 'uf001'
as a simple string in python?

The characters uf001 are not actually present in the string, so you can't just slice them off. You can do
repr(s)[-6:-1]
or
'u' + hex(ord(s[-1]))[2:]

Since you want the actual string (as seen from comments) , just get the last character [-1] index , Example -
>>> a = u'splunk>\xae\uf001'
>>> print(a)
splunk>®ï€
>>> a[-1]
'\uf001'
>>> print(a[-1])
ï€
If you want the unicode representation (\uf001) , then take repr(a[-1]) , Example -
>>> repr(a[-1])
"'\\uf001'"
\uf001 is a single unicode character (not multiple strings) , so you can directly get that character as above.
You see \uf001 because you are checking the results of repr() on the string, if you print it, or use it somewhere else (like for files, etc) it will be the correct \uf001 character.

u'' it is how a Unicode string is represented in Python source code. REPL uses this representation by default to display unicode objects:
>>> u'splunk>\xae\uf001'
u'splunk>\xae\uf001'
>>> print(u'splunk>\xae\uf001')
splunk>®
>>> print(u'splunk>\xae\uf001'[-1])

If your terminal is not configured to display Unicode or if you are on a narrow build (e.g., it is likely for Python 2 on Windows) then the result may be different.
Unicode string is an immutable sequence of Unicode codepoints in Python. len(u'\uf001') == 1: it does not contain uf001 (5 characters) in it. You could write it as u'' (it is necessary to declare the character encoding of your source file on Python 2 if you use non-ascii characters):
>>> u'\uf001' == u''
True
It is just a different way to represent exactly the same Unicode character (a single codepoint in this case).
Note: some user-perceived characters may span several Unicode codepoints e.g.:
>>> import unicodedata
>>> unicodedata.normalize('NFKD', u'ё')
u'\u0435\u0308'
>>> print(unicodedata.normalize('NFKD', u'ё'))
ё

Bytes in a unicode Python string

In Python 2, Unicode strings may contain both unicode and bytes:
a = u'\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \xd0\xb5\xd0\xba'
I understand that this is absolutely not something one should write in his own code, but this is a string that I have to deal with.
The bytes in the string above are UTF-8 for ек (Unicode \u0435\u043a).
My objective is to get a unicode string containing everything in Unicode, which is to say Русский ек (\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \u0435\u043a).
Encoding it to UTF-8 yields
>>> a.encode('utf-8')
'\xd0\xa0\xd1\x83\xd1\x81\xd1\x81\xd0\xba\xd0\xb8\xd0\xb9 \xc3\x90\xc2\xb5\xc3\x90\xc2\xba'
Which then decoded from UTF-8 gives the initial string with bytes in them, which is not good:
>>> a.encode('utf-8').decode('utf-8')
u'\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \xd0\xb5\xd0\xba'
I found a hacky way to solve the problem, however:
>>> repr(a)
"u'\\u0420\\u0443\\u0441\\u0441\\u043a\\u0438\\u0439 \\xd0\\xb5\\xd0\\xba'"
>>> eval(repr(a)[1:])
'\\u0420\\u0443\\u0441\\u0441\\u043a\\u0438\\u0439 \xd0\xb5\xd0\xba'
>>> s = eval(repr(a)[1:]).decode('utf8')
>>> s
u'\\u0420\\u0443\\u0441\\u0441\\u043a\\u0438\\u0439 \u0435\u043a'
# Almost there, the bytes are proper now but the former real-unicode characters
# are now escaped with \u's; need to un-escape them.
>>> import re
>>> re.sub(u'\\\\u([a-f\\d]+)', lambda x : unichr(int(x.group(1), 16)), s)
u'\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \u0435\u043a' # Success!
This works fine but looks very hacky due to its use of eval, repr, and then additional regex'ing of the unicode string representation. Is there a cleaner way?

In Python 2, Unicode strings may contain both unicode and bytes:
No, they may not. They contain Unicode characters.
Within the original string, \xd0 is not a byte that's part of a UTF-8 encoding. It is the Unicode character with code point 208. u'\xd0' == u'\u00d0'. It just happens that the repr for Unicode strings in Python 2 prefers to represent characters with \x escapes where possible (i.e. code points < 256).
There is no way to look at the string and tell that the \xd0 byte is supposed to be part of some UTF-8 encoded character, or if it actually stands for that Unicode character by itself.
However, if you assume that you can always interpret those values as encoded ones, you could try writing something that analyzes each character in turn (use ord to convert to a code-point integer), decodes characters < 256 as UTF-8, and passes characters >= 256 as they were.

(In response to the comments above): this code converts everything that looks like utf8 and leaves other codepoints as is:
a = u'\u0420\u0443\u0441 utf:\xd0\xb5\xd0\xba bytes:bl\xe4\xe4'
def convert(s):
try:
return s.group(0).encode('latin1').decode('utf8')
except:
return s.group(0)
import re
a = re.sub(r'[\x80-\xFF]+', convert, a)
print a.encode('utf8')
Result:
Рус utf:ек bytes:blää

The problem is that your string is not actually encoded in a specific encoding. Your example string:
a = u'\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \xd0\xb5\xd0\xba'
Is mixing python's internal representation of unicode strings with utf-8 encoded text. If we just consider the 'special' characters:
>>> orig = u'\u0435\u043a'
>>> bytes = u'\xd0\xb5\xd0\xba'
>>> print orig
ек
>>> print bytes
ек
But you say, bytes is utf-8 encoded:
>>> print bytes.encode('utf-8')
ек
>>> print bytes.encode('utf-8').decode('utf-8')
ек
Wrong! But what about:
>>> bytes = '\xd0\xb5\xd0\xba'
>>> print bytes
ек
>>> print bytes.decode('utf-8')
ек
Hurrah.
So. What does this mean for me? It means you're (probably) solving the wrong problem. What you should be asking us/trying to figure out is why your strings are in this form to begin with and how to avoid it/fix it before you have them all mixed up.

You should convert unichrs to chrs, then decode them.
u'\xd0' == u'\u00d0' is True
$ python
>>> import re
>>> a = u'\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \xd0\xb5\xd0\xba'
>>> re.sub(r'[\000-\377]*', lambda m:''.join([chr(ord(i)) for i in m.group(0)]).decode('utf8'), a)
u'\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \u0435\u043a'
r'[\000-\377]*' will match unichrs u'[\u0000-\u00ff]*'
u'\xd0\xb5\xd0\xba' == u'\u00d0\u00b5\u00d0\u00ba'
You use utf8 encoded bytes as unicode code points (this is the PROBLEM)
I solve the problem by pretending those mistaken unichars as the corresponding bytes
I search all these mistaken unichars, and convert them to chars, then decode them.
If I'm wrong, please tell me.

You've already got an answer, but here's a way to unscramble UTF-8-like Unicode sequences that is less likely to decode latin-1 Unicode sequences in error. The re.sub function:
Matches Unicode characters < U+0100 that resemble valid UTF-8 sequences (ref: RFC 3629).
Encodes the Unicode sequence into its equivalent latin-1 byte sequence.
Decodes the sequence using UTF-8 back into Unicode.
Replaces the original UTF-8-like sequence with the matching Unicode character.
Note this could still match a Unicode sequence if just the right characters appear next to each other, but it is much less likely.
import re
# your example
a = u'\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \xd0\xb5\xd0\xba'
# printable Unicode characters < 256.
a += ''.join(chr(n) for n in range(32,256)).decode('latin1')
# a few UTF-8 characters decoded as latin1.
a += ''.join(unichr(n) for n in [2**7-1,2**7,2**11-1,2**11]).encode('utf8').decode('latin1')
# Some non-BMP characters
a += u'\U00010000\U0010FFFF'.encode('utf8').decode('latin1')
print repr(a)
# Unicode codepoint sequences that resemble UTF-8 sequences.
p = re.compile(ur'''(?x)
\xF0[\x90-\xBF][\x80-\xBF]{2} | # Valid 4-byte sequences
[\xF1-\xF3][\x80-\xBF]{3} |
\xF4[\x80-\x8F][\x80-\xBF]{2} |
\xE0[\xA0-\xBF][\x80-\xBF] | # Valid 3-byte sequences
[\xE1-\xEC][\x80-\xBF]{2} |
\xED[\x80-\x9F][\x80-\xBF] |
[\xEE-\xEF][\x80-\xBF]{2} |
[\xC2-\xDF][\x80-\xBF] # Valid 2-byte sequences
''')
def replace(m):
return m.group(0).encode('latin1').decode('utf8')
print
print repr(p.sub(replace,a))
###Output
u'\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \xd0\xb5\xd0\xba
!"#$%&'()*+,-./0123456789:;<=>?#ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~\x7f\x80\x81\x82\x83\x84\x85\x86\x87\x88\x89\x8a\x8b\x8c\x8d\x8e\x8f\x90\x91\x92\x93\x94\x95\x96\x97\x98\x99\x9a\x9b\x9c\x9d\x9e\x9f\xa0\xa1\xa2\xa3\xa4\xa5\xa6\xa7\xa8\xa9\xaa\xab\xac\xad\xae\xaf\xb0\xb1\xb2\xb3\xb4\xb5\xb6\xb7\xb8\xb9\xba\xbb\xbc\xbd\xbe\xbf\xc0\xc1\xc2\xc3\xc4\xc5\xc6\xc7\xc8\xc9\xca\xcb\xcc\xcd\xce\xcf\xd0\xd1\xd2\xd3\xd4\xd5\xd6\xd7\xd8\xd9\xda\xdb\xdc\xdd\xde\xdf\xe0\xe1\xe2\xe3\xe4\xe5\xe6\xe7\xe8\xe9\xea\xeb\xec\xed\xee\xef\xf0\xf1\xf2\xf3\xf4\xf5\xf6\xf7\xf8\xf9\xfa\xfb\xfc\xfd\xfe\xff\x7f\xc2\x80\xdf\xbf\xe0\xa0\x80\xf0\x90\x80\x80\xf4\x8f\xbf\xbf'
u'\u0420\u0443\u0441\u0441\u043a\u0438\u0439 \u0435\u043a
!"#$%&'()*+,-./0123456789:;<=>?#ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~\x7f\x80\x81\x82\x83\x84\x85\x86\x87\x88\x89\x8a\x8b\x8c\x8d\x8e\x8f\x90\x91\x92\x93\x94\x95\x96\x97\x98\x99\x9a\x9b\x9c\x9d\x9e\x9f\xa0\xa1\xa2\xa3\xa4\xa5\xa6\xa7\xa8\xa9\xaa\xab\xac\xad\xae\xaf\xb0\xb1\xb2\xb3\xb4\xb5\xb6\xb7\xb8\xb9\xba\xbb\xbc\xbd\xbe\xbf\xc0\xc1\xc2\xc3\xc4\xc5\xc6\xc7\xc8\xc9\xca\xcb\xcc\xcd\xce\xcf\xd0\xd1\xd2\xd3\xd4\xd5\xd6\xd7\xd8\xd9\xda\xdb\xdc\xdd\xde\xdf\xe0\xe1\xe2\xe3\xe4\xe5\xe6\xe7\xe8\xe9\xea\xeb\xec\xed\xee\xef\xf0\xf1\xf2\xf3\xf4\xf5\xf6\xf7\xf8\xf9\xfa\xfb\xfc\xfd\xfe\xff\x7f\x80\u07ff\u0800\U00010000\U0010ffff'

I solved it by
unicodeText.encode("utf-8").decode("unicode-escape").encode("latin1")