How does mathematics binary work? What is math binary

Binary. In the 18th century, Leibniz, a German master of mathematical philosophy, read the composition structure of Bagua from the Latin translation of the Book of Changes sent to him by his missionary friend Bowitt, and was surprised to find that its basic prime number (0) (1), that is, the yin and yang lines of the Book of Changes, its carry system is binary, and he believes that this is the most advanced mathematical base system in the world.

In the 20th century, which is known as one of the important symbols of the third scientific and technological revolution, the invention and application of computers, the mode of operation is binary. It not only proves that Leibniz's principle is correct, but also proves that I Ching mathematics is remarkable.

Binary numbers. One, binary number notation.

Binary is a system of numbers that is widely used in computing technology. Binary numbers are numbers represented by two numbers, 0 and 1. Its base is 2, the carry rule is "every two into one", and the borrowing rule is "borrow one as two".

Binary numbers are also based on position notation, and their bit weights are based on 2 powers. For example, a binary number whose weights are in the order of -2. For integers with n digits, binary numbers with m decimal places are expressed by a weighted coefficient formula, which can be written as:

n）2＝an-1×2n-1+an-2×2n-2+……a1×21+a0×20+a-1×2-1+a-2×2-2

+a-m×2-m＝

where aj denotes the coefficient of the j-th position, which is a number between 0 and 1.

Binary numbers can generally be written as: (an-1an-2....

Example 1102] Write the binary number in the form of a weighted coefficient.

Solution: (2. Addition and multiplication of binary numbers.

The basic rules of arithmetic operations on binary numbers are very similar to those for decimal numbers. The most commonly used are addition and multiplication.

1.Binary addition.

There are four cases: 0+0 0

1+1 0 is rounded to 1

Example 1103] Find the sum of (1101)2+(1011)2.

Solution: 1 1 0 1

2.Binary multiplication.

There are four cases: 0+0 0

Example 1104] Find the product of (1110)2 times (101)2.

Solution: 1 1 1 0

1 0 0 0 1 1 0 Lookout Lord, thank you.

There are only 1 and 0 symbols in binary. The principle is that every two into one, as in the decimal system in our lives. Decimal and binary conversion: 0=0, 1=1, 2=10, 3=11, 4=100....Hope it helps.

In fact, it is every 2 into 1, such as 1+1=10

The basic principles of binary notation.

Binary is a system of numbers that is widely used in computing technology. Binary data is a number represented by two numbers, 0 and 1. Its cardinal number is 2, the carry rule is "every two into one", and the borrowing rule is "borrow one to become two", which was discovered by Leibniz, a German master of mathematical philosophy in the 18th century.

Current computer systems use basically binary systems, and data is stored in computers mainly in the form of complements. Binary in a computer is a very tiny switch, with "on" for 1 and "off" for 0.

The invention and application of the computer, which is known as one of the important symbols of the third scientific and technological revolution in the 20th century, because the digital computer can only recognize and process the data determined by '0''1' symbol string. The mode of operation is binary.

The 19th-century Irish logician George Bull's thought process on logical propositions was translated into pairs of symbols"0''.''1''In some kind of algebraic calculus, binary is a base system that is a base of every 2 digits.

Because it uses only two number symbols, it is very simple and convenient and easy to implement electronically.

Summary. Hello, mathematical binary is a numbering system based on 2 in mathematics and number circuits, and it is a binary system that represents the system with 2 as the base.

What is math binary

Hello, mathematical binary is a numbering system based on 2 in mathematics and number circuits, and it is a binary system that represents the system with 2 as the base.

The base system is a system of notation at the position of the base b (where b is a positive natural number, called the cardinal number), and the b basic symbols (or numbers) correspond to the smallest b natural numbers including 0. To produce other numbers, the position of the symbol in the number is used. The sign of the last digit is multiplied by b by its value in the left digit with its own value

Binary data also uses position notation, and its bit weight is a power of 2. For example, binary data, every 2 into 1

Binary to decimal method: "Sum by weight", the specific steps of this method are to first write the binary numbers into a weighted coefficient formula, and then sum them according to the decimal addition rules.

Convert decimal to binaryA decimal number is converted into a binary number, which is divided into integer parts and decimal parts, converted separately, and finally combined together.

Each bit of a number has a specific value.

Decimal number, the "value" of each bit is： .Thousand, hundred, ten, one .

The rule of entering (borrowing) is "every ten into one".

8031, that is: 8 thousands, 0 hundreds, 3 tens, 1 one.

Binary numbers, the "values" of the individual bits are： .Eight, four, two, one...

The rule of entering (borrowing) is "every two into one".

1101, that is: 1 eight, 1 four, 0 two, 1 one.

Taken together, it is: 13 in decimal.

There's a bunch of apples here:

You use decimal and count:

Piece.

Use binary again, count it:

Modify the cover.

After understanding the above, there is "careful addition, subtraction, multiplication, division and non", and it is not a problem.

Binary is a very old base system, and at that time, computers had not yet been born.

Later, computers"On the side" binary, there are brilliant achievements.

Two-entry cover mountain rental system: the trillions counting system based on 2 is only destroyed.

You're talking about arithmetic operations on binary numbers.

The arithmetic operation of binary numbers is very simple, and its basic operation is addition. In computers, after the introduction of complement representation and some control logic, binary subtraction, multiplication and division operations can be realized by addition.

1) Binary addition operations.

There are only four rules of addition for binary numbers: 0+0=0 0+1=1 1+0=1 1+1=10 (rounded to the high position).

Example: Calculate the sum of 1101+1011.

As can be seen from the equation, when two binary numbers are added, each bit has a maximum of three digits: the number to be added, the number to be added, and the number to carry from the lower place. According to the addition algorithm, the sum of the base addition and the carry to the high position can be obtained.

2) Subtraction of binary numbers.

There are only four subtraction algorithms for binary numbers: 0-0=0 0-1=1 (borrowing from the high position) 1-0=1 1-1=0

Example: Calculate the difference of 11000011 00101101.

As we can see, when two binary numbers are subtracted, each bit has a maximum of three digits: the subtracted digit, the subtracted digit, and the borrowed digit to the higher position. According to the subtraction algorithm, the difference between the subtraction of the base and the borrowing to the high position can be obtained.

3) Multiplication of binary numbers.

There are only four rules of multiplication for binary numbers: 0*0=0 0*1=0 1*0=0 1*1=1

Example: Calculate the product of 1110 1101.

From the equation, it can be seen that two binary numbers are multiplied, and if the corresponding digit multiplier is 1, then the partial product is the multiplier; If the corresponding digit multiplier is 0, then the partial product is all 0The number of partial products is equal to the number of digits of the multiplier. Calculating the product of two binary numbers by the displacement accumulation method may seem more cumbersome than traditional multiplication, but it is accepted by computers.

The function of the accumulator is to perform addition operations and save their results, which is an important part of the combinator.

4) Division operations on binary numbers.

There are only four rules of division for binary numbers: 0 0=0 0 1=0 1 0=0 1 0=0 (meaningless) 1 1=1

Example: Calculate the quotient and remainder of 100110 110.

From the equation, it can be seen that (100110)2 (110)2 has the quotient (110)2, and the remainder (10)2However, to implement the above division process in the computer, it is impossible to rely on observation to judge whether each step is "enough to subtract", and it needs to be modified, and the "recovery remainder method" and "non-recovery remainder method" are usually used, which will not be introduced here.

Binary: A system of numbers widely used in computing techniques.

Binary data is a number represented by two numbers, 0 and 1.

Its base is 2, the carry rule is "every two into one", and the borrowing rule is "borrow one as two".

The advantages and disadvantages of binary are obvious: the advantage is that there are only two digits 0 and 1, so each digit can be represented by any element with two different steady states; The basic operation rules are simple and the operation is convenient.

The disadvantage is that when a number is represented in binary, there are many digits.

Therefore, in actual use, the decimal system is mostly used before feeding into the number system.

Features of binary:

1. The technical implementation is simple. A computer is composed of logic circuits, which usually have only two states, the switch on and off, which can be represented by "1" and "0".

2. Simplify the operation rules. There are three combinations of two binary numbers and product operations, and the operation rules are simple, which is conducive to simplifying the internal structure of the computer and improving the operation speed.

3. Suitable for logical operations. Logical algebra is the theoretical basis of logical operations, and binary has only two numbers, which coincides with the "true" and "false" in logical algebra.

4. It is easy to convert, and binary and decimal numbers are easy to convert to each other.

5. The binary representation of data has the advantages of strong anti-interference ability and high reliability. Because each piece of data has only two states, high and low, when it is disturbed to a certain extent, it can still be reliably distinguished.