binary computing technology is widely used in a number system. Binary data is 0 and 1 to represent the number two digital. Its base is 2, the carry rule is
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steps outlined characteristics of computing addition operation procedure subtraction multiplication division step step binary binary code causes the computer 1. Easier said 2. Op conversion of a simple binary decimal conversion technique Skills binary and octal binary hexadecimal conversion techniques outlined every binary number is 2 binary binary system, 0,1 is the basic operator; the basis of binary computing. Computer is based on binary. In the early design of the common band is mainly decimal (because we have ten fingers, so
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decimal is a more reasonable choice, ten fingers can represent numbers, until long after the concept of 0 emerge, it is 1-10, not 0-9). Computer appears, use the tube is too complex to represent ten states, all of the computer, only two basic states, on and off. In other words, the two states determines the tube to tube-based computer to represent numbers and binary data. There are 8 common binary and hexadecimal 16 hexadecimal, in computer science, often used 16-band, and very little use of the decimal, which is 16 hex and binary as a natural contact: 4 binary bits can represent numbers from 0 to 15, which happens to be a 16-bit hexadecimal data can be represented, that is, the binary converted into 16 as long as each 4-bit binary conversion on it. Binary A word is a basic computer storage unit, according to the different computer word, the word has a different number of bits, the modern computer word length is generally 32, that is, a word of bits is 32. Byte is 8 bits of data unit, a byte of data can represent 0-255. 32-bit word length for the modern computer, a word is equal to 4 bytes, for the early 16's computer, a word is equal to 2 bytes. Addition 0 +0 = 0,0 +1 = 1 +0 = 1,1 +1 = 10 0-0 = 0,1-0 = 1,1-1 subtraction 0,0-1 =- 1,10100-1010 = 1010 = 0 × 0 = multiplication 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,
skechers shoes, if a binary number (integer) number of the first value is zero, then the number is odd; and if the bit is zero, then the number is even.
binary number
2,
shape up shoes, 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 number is equal to 2n. 4, if a binary zero to the first n-bit (but does not contain spaces n) are one and the other of you are zero, then this number is equal to 2n-1. 5, all the bits of a binary left shift result is multiplied by the number two. 6, will be an unsigned binary number of all bits of the result of a right equivalent to the number divided by two (this does not apply to have signed.) The remainder will be rounded down (rounddown) 7, the two n-bit binary complementary to each other may require 2 * n-bit to save 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, a binary number to invert all the bits (that is, a change of all zero, all the zero to one) is equivalent to the number of negation (changing sign) then the result of minus one. 10, will be any given number of bits that the largest unsigned binary number plus one of the result is always zero. 11, zero decline (minus one) the result is always a given that the maximum number of bit unsigned binary number. 12, n bits can represent different combinations of 2n. 13, number 2 years contains n bits, all bits are one. Binary computing operations in addition to arithmetic, but also can have a logic operation.
binary number
The following were to be introduced. Four fundamental operations of binary numbers and decimal numbers as binary numbers, the same can add, subtract, multiply and divide arithmetic. The algorithm rules are as follows: add operation: 1 = 0 0 = 0,0 1,1 1,1 0 = 1 = 10, # every 2 into 1; subtract 1-1 = 0,1-0 = 1,0 -0 = 0,0-1 = 1, # 1, when the high by 2; Multiplication: 0 × 0 = 0,0 × 1 = 0,1 × 0 = 0,1 × 1 = 1, # only if it is Addition operation as follows: (1) The first is the most right-digital-bit addition. Here are addend addend and the last one are (2) and then add the last second. Here the inverse of the addend and the second summand are to bit (3) further added to the bottom third. Here the inverse of the addend and the second summand are all Add (4) Finally, adding the highest level. Here are addend addend and the highest bit is One can only have one number, so it is necessary to move on again, First, the last one to the last second by the because the bit the same as lent to the last Countdown to the third one on them by the bit is bit the reciprocal of the fifth for the original to its high (sixth last) by bit after the the number of addition and subtraction computation method, in fact, is the same reason they are also the one to one. In addition of decimal numbers, into the as a decimal number. multiplication steps in the binary number multiplicand,
skechers tone ups, the lowest level and multiplying all the bits, the lowest since the multiplier is . 2, multiplying the results of the high-three were for the This is a multiplier of This is one of the multiplier to The results obtained by bit (with the decimal numbers the same way as multiplication), the result (1110) 2 × (0110) 2 = (1010100) 2. division step (1) First, with the equivalent of 011 life, we often use a variety of codes, such as the provinces of card number, telephone number, zip code, etc. These codes are formed by a decimal number. Similarly, in the computer used by a number of bits, consisting of short binary encoding 【 encoding】 to represent letters, symbols, characters, color and other non-numerical information. in order to express different types of information, people come up with a variety of coding schemes. which, ASCII code is commonly used by a character encoding scheme information, It uses 8
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bit binary representation of various letters and symbols, for example: that B A 01000010 01000001 character that many words, so the current 16-bit binary representation with the Chinese characters commonly used, for example: 10,100,111 11000000 means two bytes to store a character code. with the same binary, binary code is used to represent information inside the computer as a means of dealing with people when the computer normally, and simply do not ignore it. We still use the way people used to enter or output information from computer automatically during the conversion to complete. instances of the control binary decimal → 16 → 10000 46 → 101110 99 → 1100011 888 → 1101111000 7654 → 1110111100110 10000 → 10011100010000 Note: General in order to distinguish binary and decimal, and then After the binary number with a composition, that is: 0.1.2.3.4.5.6.7.8.9 [we generally call the base] is the number, but they represent different positions in the weight is not the same Well, as 111, is 1 but is not the same, which involves the concept of the right position, and using the following example to illustrate. a decimal Results 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) [a statement: (N) indicates the N th power] in this number, some of the same number as in a different location, the size of the value they represent is different, you figure the size of the value represented by bit the right to decide. bit right is a power value, power of the base as the base binary notation (in this case for 1 0), while the index number of the digits in the position to decide. above the decimal number, from left to right you were the right number of bits: 10 (3), 10 (2) .10 (1 ), 10 (0), 10 (-1), 10 (-2). General
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terms of the binary system in a number of Members to 1, the representative figure of the magnitude called the right place. If the right bit 456 which is when you when the numerical value of 1, 456 of the 4-bit right is 10 (2), 5-bit right is 10 (1), 6 is 10 bit right (0). In addition to the right of the decimal place count is another important concept is the base, the base is well understood, that is, in binary notation symbols used by the number of different basic counting system called the base, such as the decimal is 1.2.3.4.5.6.7.8.9.0 these ten, relative to two base binary terms: 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 two concepts can be drawn from the above the following formula: [The following will detail the name] N can be expressed as a decimal base: 0.1.2 ...... N-2.N- 1 N can generally be said right hex: N (X) [X is the X power, X is a number in its series, the location of] 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 Base: 0 to 9, every decade a binary: there are 2 base: 0 ~ ~ 1, every two further octal: There are eight base: 0 to 7, every eight further hex: 16 Base: 0 ~ ~ 9, A, B, C, D, E, F (A = 10, B = 11, C = 12, D = 13, E = 14, F = 15), every one as hexadecimal start Aberdeen, we learn from the Xiaowa decimal, use of life is extensive, a the number of single mode of thinking that we are only so many people think of a decimal. talk to you in the following most frequently used computer hexadecimal numbers, so that everyone open mind, do not stop at the rigid thinking patterns. computer most frequently used is the only recognize a few CPU system, it is binary. The computer is a machine to process information and information processing on the premise that the information says. the computer is the binary representation of information in digital code. In other words, various types of information (numbers, 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 the last to the CPU that will only 0 and 1, and sometimes feel that people who design the computer too much, so the two numbers will be able to come up with something perfect, and this is wisdom, in fact, the final analysis, the CPU will hundreds of instruction only, in the superposition of layers of software and systems under the computer we simply do not understand what kind of house? fact, no two states 0 and 1 is just friends. the reasons for a binary computer. easier said binary Only the number of transistor turn-on that the device can be expressed in binary it is very difficult. 2. computing simple binary arithmetic is extremely simple addition and multiplication operations only have three rules (0 +0 = 0,0 +1 = 1,
shape ups skechers,1 +1 = 1 0 and 0 × 0 = 0,0 × 1 = 0,
skechers shape ups,1 × 1 = 1), operation is not easy to go wrong. [In fact, computer processing, arithmetic operations are additions and shifts, and no multiplication and division, such as the left one to become a 11B 110B, 11B is the decimal 3,
skechers shoes online, while the 110B is 6, see if it is equal to by two, take the left, right on the addition, haha, fun bar] In addition, the binary number advantage, but after all we are used to daily life in decimal, in order to be universal, it is necessary to convert it to decimal. As to why the octal and hexadecimal with it? is simply because it is a power of 2, 2 (3) = 8,2 (4) = 16, so that to facilitate the calculation and reading the binary. for other simple binary to decimal conversion, the following example: In this elaborate, there are abbreviations commonly used binary This is in order not to be confused, such as decimal general at the end, add a letter D [general practice is not added], binary plus a B, octal Q, H. hex 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 =
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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) The binary to decimal conversion to other more difficult task, oh, but the method is there, and many ways, a more commonly used in this presentation, easy people to grasp. decimal to binary conversion technique can only be an example, the text says unclear, usually a decimal integer and fractional parts separately. 1, the integer number system conversion; - a 2, the remainder is the binary equivalent of the lowest. (2) the quotient divided by the previous step radix of 2, the remainder is the binary equivalent of the second low. (3) Repeat step 2 until the last obtained business is equal to 0. The second addition to the remainder obtained is the binary number of Members, the last remainder is the highest-bit binary and hexadecimal octal binary conversion techniques starting from the lowest bit that each of its three corresponding to decimal conversion less than three high octal, binary zeros Similarly starting from the lowest bit into each of four hexadecimal decimal that corresponds to its high less than four, zero padding, such as (1001100) 2 = (114) 8 = (4C) 16 additional entries Atlas Atlas Open Category: binary system, translation the number of
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