binary computing technology is widely used in a number system. Binary data is 0 and 1 to represent the number two digital. Its base 2, binary rule is
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Features operations overview of the steps subtraction addition operation multiplication step step step binary division binary coded reason for a computer. Easier said 2 simple binary operators convert decimal conversion technique binary and octal binary skills hex binary conversion technique is outlined in every 2 binary decimal system, 0,1 is the basic operator; computing foundation binary. Computer is based on the binary. Commonly used in the early design of the main band is decimal (because we have ten fingers, sobinary
decimal is a more reasonable choice, with your fingers can be expressed as ten digits, 0 concept until much later emerge, it is 1-10, not 0-9). Computer occurred, said the ten kinds of state using the tube to be too complicated, so all of the computer, only two basic states, on and off. In other words, the two states determines the tube to tube-based computer used to represent binary numbers and data. Commonly used binary and 8 decimal, and hexadecimal, in computer science, often used hexadecimal, and decimal use very little, because the hexadecimal and binary have a natural connection: four binary bits can represent numbers from 0 to 15, which happens to be a hexadecimal digit can represent the data, that is, convert the binary as long as every four hexadecimal conversion on it. Binary A word is the basic storage unit in the computer, according to the different computer word length, word has a different number of bits, modern computers are generally 32-bit word length, that is, a word is 32 bits. Byte is 8 bits of data unit, a data byte can represent 0-255. For 32-bit word length of the modern computer, a word is equal to 4 bytes, for the earlier 16-bit computer, a word is equal to 2 bytes. Addition 0 +0 = 0, 0 +1 = 1 +0 = 1, 1 +1 = 10 subtraction 0-0 = 0,1-0 = 1,1-1 = 0,0-1 = 1,10100 - 1010 = 1010 Multiplication 0 × 0 = 0,0 × 1 = 1 × 0 = 0,1 × 1 = 1 division 0 ÷ 1 = 0,1 ÷ 1 = 1 0 and 1 only two digital, base two. Features 1, if a binary number (integer) number of the first zero value is 1, then this number is odd; and if the bit is 0, then the number is even.binary
2, if a low-end n-bit binary number is zero, then this number can be divisible by 2n. 3, if a first n-bit binary number is one, while others of you are zero, then this is equivalent to 2 ^ n. 4, if a binary zero to the first n - 1 bits are 1, and the other of you are 0, then this is equivalent to 2 ^ n - 1. 5, all of a binary bit left shift is the result multiplied by two. 6, an unsigned binary number of all-bit right shift is equivalent to the result of a number divided by two (this number does not apply to have the symbol). Remainder will be rounded down (rounddown) 7, the two n-bit binary number complementary to each other may need 2 * n bits to store the results. 8, the two n-bit binary numbers will not add or subtract more than n 1 bits need to save the results. 9, all of a binary bit-wise inverted (that is, to all of a zero, all the zero to one) is equivalent to the number of negation (sign change) and then the results minus one. 10, to any given maximum number of bits plus an unsigned binary result is always zero. 11, zero down (by) the result is always a given that the maximum number of bit unsigned binary number. 12, n bits can represent 2n different combinations. 13, number 2 years of n bits, all bits are one. Computing the number of operations in addition to the binary arithmetic, but also can have a logic operation.binary
The following were to be introduced. The binary arithmetic binary and decimal numbers, same as you can add, subtract, multiply, and divide arithmetic. Rules of the algorithm is as follows: add operation: 0 0 = 0 = 0,0 1,1 1,1 1 = 1 = 10, # every 2 into 1; subtraction :1-1 = 0,1-0 = 1,0 -0 = 0,0-1 = 1, # 2 when the high by 1; multiplication: 0 × 0 = 0,0 × 1 = 0,1 × 0 = 0,1 × 1 = 1, # only while Addition operation as follows: (1) First is the sum of the right of digital bits. Here addend and the last summand are (2) then the second lowest sum. Here addend and summand in the penultimate position are bit (3) then add the bottom third. Here addend and summand in the penultimate position are plus (4) Finally highest sum. Addend and summand where the highest bit is One can only have one number, so the need to move forward again, First, the last one to the last second by the , the same as the bit to lent to the last the bottom third to take them on a bit is bit ) by The subtrahend is not the place, so the result is the minuend the size of the corresponding bit value, where Their reasoning is the same, and it is one to one in decimal addition, the intake of We borrow to high number of 0 bit multiply, the lowest since the multiplier is the reciprocal of the second and all the bits multiplicand multiplied, because this one is the multiplier of the same way as the number of multiplication), the result (1110) 2 × (0110) 2 = (1010100) 2. division step (1) first used the enough to be removed, so they need to take a low, eventually to be 1 continue to move forward in taking a dividend, to be , just to get the remainder as such as provinces, card number, telephone number, zip code, these codes are formed by a decimal number. Similarly, in the computer used by a number of bit binary number encoding [short] to represent the binary encoding letters, symbols, characters , color and other non-numerical information in order to express different types of information, people developed a variety of coding schemes which, ASCII code is a widely used character encoding scheme information, it is a binary number with 8< / p> bit binary number that various letters and symbols, for example: 01000001 A 01000010, said that more B Chinese words, so far with 16-bit binary number that commonly used Chinese characters, such as: 1,010,[url=http://www.uggclearanceuks.com/][b]title=ugg clearance uk[/b][/url],011,111,000,000 that Island Chinese characters. 8 bits called a byte [Byte, referred to as B] byte is the basic unit of information storage, a byte can store one letter or symbol coding, the two bytes to store a character encoding . with the same binary, binary encoding is used to represent information within a computer as a means of dealing with people and computers usually when there is no need of it, we still use the way people used to input or output information from computer during the conversion automatically to complete the Computer in a storage unit (one byte) in what is stored in binary or binary code? English Chinese characters? the fact that they identified by the program, for example, that the English character encoding 8-bit binary The highest bit is 0, and that two 8-bit binary-coded characters of the highest bit is 1, which is the difference between the storage unit where the program is stored in a basis in English or Chinese characters. instance of the control decimal → binary decimal 0 12345678910 binary 0000 0001 0010 0011 0100 0101 0110 0111 100010011010 16 → 10000 46 → 101110 99 → 1100011 888 → 1101111000 7654 → 1110111100110 10000 → 10011100010000 Note: Generally in order to distinguish binary and decimal, binary number and then adds a ...... on a number of these figures are only composed by ten, that is: 0.1.2.3.4.5.6.7.8.9 [we generally call the base] are all these numbers, but they represent a different position Oh, the weight is not the same as 111, but they are not the same as 1, which relates to the concept of the right place, and using the following example to illustrate. a decimal number end 4553 .8 7 can be expressed as: 4553.87 = 4 × 10 (3) +5 × 10 (2) +5 × 10 (1) +3 × 10 (0) +8 × 10 (-1) × 7 × 10 (-2) [Statement: (N ) that the N-th power] in this number, some of the same figure as in a different location, the size of the values they represent different, you figure represents the value of the right size is determined by the bit. bit power is a power value, the power base for the binary counting system base (in this case 10), while the index number of the digits in the position to determine the above number in decimal, from left to right you the right number of bits are as follows: 10 (3), 10 (2) .10 (1), 10 (0), 10 (-1), 10 (-2).
general binary
and words, in the decimal system, you put a number in figure 1 represents the value of size is called the right place, such as 456 of their position is that when you right when the magnitude of 1, 456 in the 4-bit right is 10 (2), 5-bit power is 10 (1), 6-bit right is 10 (0) In addition to the right of the binary bit count is another important concept is the base, the base is well understood that decimal counting system in the different basic symbols used in the count of the number system is called the base, such as a decimal number is 1.2.3.4.5.6.7.8.9.0 these ten, the two relative binary base: 0 and 1, octal is: 0.1.2.3.4.5.6.7.8, hexadecimal is: 0.1.2.3.4.5.6.7.8.9.ABCDEF above two concepts can be drawn from the following formula: [The following will detail the name of] N binary base can be expressed as: 0.1.2 ...... N-2.N-1 N hex rights usually can be expressed: N (X) [X is a power of X, X is a number in its series of location] N band launched into a decimal public test: If abcdefg.hijk = a * N (6) + b * N (5) + c * N (4) + d * (3) + e * (2) + f * N (1) + g * N (0) + h * N (-1) + i * N (-2) + j * N (-3) + k * N (-4) Decimal: 10 a Base: 0 ~ ~ 9, every decade a binary: there are two base: 0 ~ ~ 1, every two further octal: There are eight base: 0 ~ ~ 7, every eight hexadecimal further: there 16 Base: 0 ~ ~ 9, A, B, C, D, E, F (A = 10, B = 11, C = 12, D = 13, E = 14, F = 15), every hex one as we learn from the beginning Xiaowa decimal Aberdeen, life is even more widespread use, a single mode of thinking to figure many of us think that only a few of this kind of band in the following for everyone to talk about the computer using the most The binary number, so that we open mind, do not stay in the static mode of thinking. computer using the most CPU is the only recognize the number system, it is binary. the computer is processing information of the machine, the premise of information processing representation of information. the computer is the binary representation of information in digital code, meaning that all types of information (number, text, sound, images) must be converted into a digital form of a binary digital code to the computer for processing. even if you move the mouse, click the keyboard, your every action and finally to the CPU that will only 0 and 1, and sometimes feel that people who design the computer too much, you can get two numbers out such a perfect thing to, this is wisdom, in fact, just a few hundred in the final analysis the CPU instruction only, in the superposition of layers of software and systems under the computer so that we simply do not understand what kind of house? in fact not that is, only two states 0 and 1 friends. the reasons for computer use binary 1 is only likely to represent a binary number ; that light switch of positive and negative, high and low potential of all, there are two opposing steady-state devices can represent a binary .., 9), in order to use the 10 states that use electronic devices is difficult to implement 2. computing simple binary arithmetic operations particularly simple addition and multiplication operations only have three rules (0 +0 = 0,0 +1 = 1,1 +1 = 1 0 and 0 × 0 = 0,0 × 1 = 0,1 × 1 = 1), when the operation is not easy to go wrong. [In fact, computer arithmetic processing when they addition and shift, and no multiplication and division, such as 11B left one becomes 110B, 11B is the decimal 3, and 110B is a 6, take a look at is not equal to two, take the left, right on the addition, Haha, fun bar] In addition, the binary number basic operations, binary can easily be two types of simple operations. decimal binary conversion techniques Although there are many advantages, but after all our daily lives are used in decimal, in order to be universal, it is necessary to convert it to decimal. As for why to use octal and hexadecimal it? It is simply because it is a power of 2, 2 (3) = 8,2 (4) = 16, such an action would facilitate the calculation and reading binary For other simple binary to decimal, the following example: elaborate here, there are band commonly used shorthand, this is not to be confused, such as decimal general at the end, add a letter D [general habits are not added], binary plus a B, octal Q, hexadecimal H. For example: 123D, 1011B, 123Q, AB9H 123D = 1 × 100 +2 × 10 +3 × 1 = 123 0.11D = 1 * 10 (-1) +1 * 10 (-2) 1011B = (1 × 8 +0 × 4 +1 × 2 +1 × 1) D = 11 0.11B =binary
1 * 2 (-1) +1 * (-2) 123Q = (1 × 64 +2 × 8 +3 × 1) D = 83 0.11Q = 1 * 8 (-1) +1 * 8 (-2) AB9H = (10 × 256 +11 × 16 +9 × 1) D = 2745 0.11H = 1 * 16 (-1) +1 * 16 (-2) and the decimal conversion is more difficult task for the other band, oh, but it is there, and a number of ways In this introduction a relatively common, easy to you to master. decimal to binary conversion technique can for example, the text can not tell, usually a decimal integer and fractional parts separately. 1, the integer number system conversion; - a base 2, the remainder is the binary equivalent of the low number of times (3) Repeat step 2 until the final quotient is equal to 0. The second addition was the remainder is the number of binary you, the last remainder is the highest bit binary and hexadecimal octal binary conversion techniques start from the lowest bit of each of its three converted to decimal is less than the corresponding high three octal, binary zeros Similarly starting from the lowest position that each of its four converted to decimal corresponds to less than four hexadecimal high, zero padding,[url=http://www.in-moncler.com][b]title=Cheap Moncler[/b][/url], such as (1001100) 2 = (114) 8 = (4C) 16 more entries Atlas Atlasentry picture (6)
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