1, the minimum unit of the computer system bit binary
In a binary computer system: 'bit (bits): the smallest unit of data storage. Abbreviated
b, also referred to as bit (bit), each binary number is a 1 or 0 bit (bit), wherein each8bit = 1 byte(bytes);
Recalling further data type in Java, such as int数据类型 = 4个byte(字节)while 1 byte(字节) = 8 bit(位); we will often say int = 32位(it plainly, is a bit as a data storage unit in the binary system). as follows
2, symbols and unsigned
Signed and unsigned numbers simply means that the positive and negative respectively, are 'bit (bit) in a binary system as a data storage unit, the most significant bit (first bit) is the sign bit, the sign bit positive number It is "0", a negative sign bit is "1."
example:
Suppose int number = 1, then the number represented in a computer system is as follows:
00000000 00000000 00000000 00000001
Similarly available, number = -1when expressed in binary as follows:
10000000 00000000 00000000 00000001
Note: The most significant bit (first bit) is the sign bit, a value of 1 because the number is a positive number, the most significant bit is 0;
3, the original binary code, anti-code complement
The original code of the original code is the number of machines, is to add a sign bit of a binary number (because the values have positive and negative points), the number of positive sign bit is 0, a sign bit is negative.
Inverted when the results of the original code correct multiplication and division with the sign bit, and in addition and subtraction when there is a problem, for example: decimal representation: 1 + (-1) = 0but with binary representation:
00000001 + 10000001 = 10000010,
The result is converted to decimal number -2. So in the original code based on the inverted invention, to solve this problem.
Complement Despite the anti-code to solve the problem of addition and subtraction of positive and negative numbers, but let this figure 0 with two kinds of "form": "0" and "-0", but this is illogical, but there should be a 0, so there are a complement.
For signed numbers in terms of :
1, a positive number of the original code, the inverted, complementary codes are the same; 2, negative = inverted its original code symbol bits unchanged, the other bit is inverted (negated meaning: 0 replaced by 1, into 1 0); 3, negative complement its inverse = +1; 4,0 inverse code, complement is 0; [1] special attention in the computer computation time, are in a manner to complement operations. 2, binary to decimal, you must use the original binary code conversion.
example:
Here we use the "signed number" to simulate the look, how in the computer operation.
(1) adding a positive number:
For example: 1 + 1, in the computer are performed as follows:
1 is the original code:
00000000 00000000 00000000 00000001
Because the "positive original code, the inverted, complementary codes are the same", so that the 1's complement of the original code = 1, the complement of the complement 1 + 1 is equal to:
00000000 00000000 00000000 00000001 + 00000000 00000000 00000000 00000001
=
00000000 00000000 00000000 00000010
00000000 00000000 0,000,000,000,000,010 (converted to decimal) = 2
(2) positive phase, dropping:
For example: 1 - 2, in the computer are performed as follows:
In fact, the computer is a subtraction operation applied to the operation, so 1--2 = 1 + (-2)
The first step: to find out one's complement (a positive number because the original code, anti-code and complement the same, so we can get directly from the complement of the original code):
1 complement:
00000000 00000000 00000000 00000001
Step two: the 2 in the original code to find out:
-2 original code:
10000000 00000000 00000000 00000010
The third step: the anti-2 code to find out:
-2-minus:
11111111 11111111 11111111 11111101
The third step: the complement -2 find out:
-2 complement:
11111111 11111111 11111111 11111110
Step Four: 1's complement of the sum and -2:
00000000 00000000 00000000 00000001 + 11111111 11111111 11111111 11111110
=
11111111 11111111 11111111 11111111
Step 5: The results complement conversion of the original code, the opposite can (if you want to convert binary to decimal, binary must be the original code)
Complement: 1,111,111,111,111,111 1,111,111,111,111,111
=
Anti-code: 1,111,111,111,111,111 1,111,111,111,111,110
=
Original code: 1,000,000,000,000,000 0,000,000,000,000,001
Step Six: the calculation result of the original binary code to decimal
Original binary code: 1,000,000,000,000,000 0,000,000,000,000,001 * 2 ^ 0 = 1 = -1
4, thinking: java Why byte ranges from -128 to 127
java byte of one byte, i.e. 8bit (bits), where the highest bit is a sign bit, a numerical value for the remaining seven. When the sign bit is 0, it indicates a positive number in the range 00000000 to 01111111 (S code form), i.e. decimal 0-127. when the sign bit is 1, it indicates negative, in the range of 10000000 ~ 11111111 (supplementary code), -128 to -1, to convert the original code is 11111111 10000001, i.e. -1. In complement, in order to avoid the presence of "-0", a predetermined 10000000 -128, the byte explains why the range is -128 to 127.
5, the Java << and >> and >>>
>>> >> and << First and java are the bitwise operators, is operated for a binary. In addition to these there are &, |, ^, ~, a few bits operator. No matter what the initial value in accordance with the band, are converted into a binary bit operations. Here mainly on Java, << and >> and >>>.
<< represents a left shift, regardless of the number of positive and negative, low complement 0
Note: The following default data type byte is 8 bits, when the left whether positive or negative, low fill 0
Positive number: R = 20 << 2
Twos complement 20: 00010100
After the two moved to the left: 01,010,000
Results: r = 80
Negative: R & lt << 2 = -20
-20 binary original code: 10010100
-20 binary one: 11101011
-20 twos complement: 11101100
Left after two's complement: 10,110,000
Anti-code: 10101111
Original code: 11010000
Results: r = -80
'>>' denotes a right shift, if the number is positive, the high bit of 0, if it is negative, the high bit of 1;
Note: The following default data type byte is 8 bits
Positive number: R = 20 >> 2
Twos complement 20: 00010100
After the two moved to the right: 00,000,101
Results: r = 5
Negative: R & lt >> 2 = -20
-20 binary original code: 10010100
-20 binary one: 11101011
-20 twos complement: 11101100
Right after the two's complement: 11,111,011
Anti-code: 11111010
Original code: 10000101
Results: r = -5
'>>>' unsigned right shift, also called a logical right shift, i.e., if the number is positive, the high bit of 0, and if the number is negative, the same high right up 0
Note: The following default data type bit int 32
Positive number: R = 20 >>> 2
Results with the same r = 20 >> 2;
Negative: R & lt >>> 2 = -20
-20 original code: 1,000,000,000,000,000 0,000,000,000,010,100
Anti-code: 1,111,111,111,111,111 1,111,111,111,101,011
Complement: 1,111,111,111,111,111 1,111,111,111,101,100
Right: 0,011,111,111,111,111 1,111,111,111,111,011
Results: r = 1073741819
Finally, if there is insufficient or is not correct, please correct me criticism, grateful!
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