About binary number subtraction operations 20

The above statement is wrong.

How to calculate the binary of 1100 111.

It should be 1100 111 = 1100 + (111) to calculate the complement of (111);

111) = (1111) 2 original code (signed bits) = (1001) supplement.

1100 111 = 1100 + 1001 = 0101, the sign bit is"0", which means that the result is positive, which means that it is 101, which is 5

The first step is to determine the number of digits, such as 5-bit base. Then first calculate the complement of -00111: 11001

Then 01100 + 11001 = 100101Because it is a 5-bit base binary, the first 1 is rounded to 00101, which is 5

If it is 6 digits, the complement of -000111: 111001, 001100+111001=1000101, round the first 1, get 000101, that is, 5

You can also set it to 7-bit, 8-bit, etc., and do the same. But note that it can't be set to 4 digits, because the first bit is the sign bit, 1100 is a positive number, and 4 digits will become the complement of -0100. It's negative.

This is what the standard approach should be.

It's the same as general subtraction, except that when borrowing the previous digit, borrowing one is used as two.

Combining the first floor and the second floor is the perfect answer.

Convert to decimal first:

So, the answer is 101

I learned it when I was in school, and now I forget it, it's a shame.

Isn't it similar to the base decimal?

The binary addition and subtraction algorithm is: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry to the high position); Binary subtraction: 0-0=0, 10-1=1 (borrowing to the high position) 1-0=1, 1-1=0 (modulo binary addition or XOR).

Multiplication of binary: 0 * 0 = 0 0 * 1 = 0,1 * 0 = 0,1 * 1 = 1 Binary division: 0 0 = 0,0 1 = 0,1 0 = 0 (meaningless), 1 1 = 1.

Logical operations binary or operation: 1 gets 1 binary and operation: 0 gets 0 binary non-operation:

Everybody's negation is the basic operator. Because it uses only two number symbols, it is very simple and convenient and easy to implement electronically.

The first digit from right to left represents the 0th power of 2, the second digit represents the 1st power of 2, and the nth digit represents the n-1st power of 2. 1 can be understood as having and 0 as none.

Binary Conversion:

The method of converting decimal to binary is to convert integers to remainder by continuous division (short division) and reverse order until the quotient is 0. Decimal conversion: Continuous multiplication base (i.e., 2) rounding and sequential arrangement method are used. Example(。

The specific steps: ,, then the forward rounding gets (.

The above content refers to: Encyclopedia - Binary Algorithm.

Binary addition and subtraction algorithm:

Binary arithmetic arithmetic operation binary addition: 0+0=0,0+1=1 ,1+0=1, 1+1=10 (carry to the high position);

Binary subtraction: 0-0=0, 10-1=1 (borrowing to the high position) 1-0=1, 1-1=0 (modulo binary addition or XOR).

Multiplication of binary: 0 * 0 = 0 0 * 1 = 0,1 * 0 = 0,1 * 1 = 1 Binary division: 0 0 = 0,0 1 = 0,1 0 = 0 (meaningless), 1 1 = 1.

Logical operation binary or operation: meet 1 to get 1 binary and operation: meet 0 to get 0 binary non-operation: you take the negation.

Binary to other base:

1) Binary to decimal system: the base number is multiplied by the weight, and then added, and the number of digits is 0 can be omitted when simplifying the operation, (because 0 multiplied by other numbers that are not 0 are all 0). The same goes for decimal parts, but with less precision.

2) Binary to octal: The "three-digit union method" (grouped by every three digits from the decimal point to the left and right sides, and 0 is added to the shortage) can be easily converted. Example: Convert a binary number ( to an octal number. (

3) Binary to hexadecimal: the use of the "four-digit union method", the integer part starts from the low bit, every four-digit binary number is a group, and the last less than four digits, then add 0 in the high position to make up four digits, or not to make up 0; The decimal part starts from the high position, every four binary digits is a group, and if there are less than four digits, you must add 0 to the low position to make up four digits, and then replace it with the corresponding hexadecimal number, and then write the corresponding hexadecimal number in order.

1. Binary subtraction:

0 0 0,10 1 1 (borrow from the high position) 1 0 1,1 1 0 (modulo 2 addition or XOR).

2. Binary addition:

0 0 0 0 0 1 1 ,1 0 1, 1 1 10 (carry to the high position).

3. Such as splitting binary multiplication:

4. Binary division:

0 0 0, 0 1 0, 1 0 0 (meaningless), 1 1 1.

Binary: 10101010 + 00101010 = 11010100.

1. The addition of binary is every two into one;

2. There are only four formulas for binary addition: 0+0=0;0+1=1；1+0=1；1+1=10；

00101010 according to the above calculation results should be: 11010100.

Erdan guessing system: 10101010 + 00101010 = 11010100.

Operation. 1. Addition.

There are four cases of binary addition: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (0 is rounded to 1).

2. Multiplication. There are four cases of binary multiplication: 0 0=0, 1 0=0, 0 1=0, 1 1=1.

3. Subtraction. There are four cases of binary subtraction: 0 0 = 0, 1 0 = 1, 1 1 = 0, 0 1 = 1.

4. Division. There are two cases of binary division (the divisor can only be 1): 0 1 = 0 and 1 1 = 1.

Let's talk to you first.

What is "du" under bai

"Decimal system": When it comes to the decimal system, for example, the DAO takes the decimal system as a return example, and we have to "forget."

Answer: "A number - 10. Why?

Because in the decimal system, there are actually only ten meaningful numbers of 0 and 9, and "ten" is actually because it meets the condition of "every ten into one", so it is represented by a number composed of "1" and "0". (By analogy, when 99 is added with 1, it is represented by "100", and so ......on.)）

Then binary is "every two into one", so in the binary world, there are only two meaningful numbers 0 and 1, so in the binary world, if you count the numbers, it is:

0,1,10 (because 1 plus 1 is 2, satisfying every two into one, so it should be written as 10.) Note: This should be pronounced as "one zero", not "ten". ）

11 (here it should be pronounced "one," not "eleven").

100 (because 11 plus 1 becomes "12", but every 2 goes into 1, so the rightmost digit becomes 0, and goes forward by a 1 and the second digit is also 1, plus the 1 that comes in from the front, it also becomes 0, and then goes forward by a 1).

Align the two numbers first, just like the first step in decimal calculation, starting with the upper and lower numbers aligned on the far right, 1+0=1, and 0+0=0.

If both numbers are not both 1s, just add them up.

Write directly below, 1=1=10, write 1 above, write 0 below.

1+1+1=11, pay attention to carrying, and so on, and the calculation is completed.

If 2700 is addition and subtraction, then only 0 and 1 are the same as normal addition and subtraction, but when encountering two into one, it is a little different from our practice system.

Addition and subtraction are not simple.

It's not the same as the decimal system, that is, the decimal 2 is equal to the binary 10. 10-1=11+1=10

Binary number division is based on the following three rules: 1=0 (1 0 is 1=1 without intention

Example: (111011)2 1011)2 The equation is as follows: (Because it is not convenient to write in the form of division operation in the web page, it is written as follows.) )

1 0 1 1 quotient 1

1 1 1 The last 1 is 1110 1 1 1 The 1 after "0" falls.

1 0 1 1 quotient 0

1 1 1 1 The last 1 is the one that fell from above.

1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 0 0 remainder 100

So (111011)2 1011)2 quotient is (101)2, and the remainder is (100)2

The so-called binary division has always been a subtraction. Binary subtraction borrows 1 from the high to get 2, so (10)2 - 1)2 = 1

I don't know if I understand what I said, I hope my use for you is closed.

1. Binary subtraction:

0 0 0,10 1 1 (borrow from the high position) 1 0 1,1 1 0 (modulo 2 addition or XOR).

2. Binary addition:

0 0 0 0 0 1 1 ,1 0 1, 1 1 10 (carry to the high position).

3. Binary multiplication:

4. Binary division:

0 0 0, 0 1 0, 1 0 0 (meaningless), 1 1 1.

It's the same as decimal, when the decimal is not enough to subtract, borrow 1 from the previous digit as 10, and borrow 1 from binary as 2.

You can also convert it to decimal and then convert it back to binary...

Binary subtraction is exactly the same as decimal system, except that it is 2 borrowed from the higher digit, not 10, and the best way for unskilled is to convert to decimal for operation, although it takes a little time, but the accuracy is guaranteed.

Binary subtraction is no different from ordinary subtraction, except that borrowing 1 at a high can only be used as 2, so there will be no problem with subtracting. The key is what to do if it is not enough to subtract, there can be negative numbers in mathematical calculations, but there are no signed bits when the program is calculated on the computer, and there are byte requirements. In this way, for non-borrowed bits, it is an ordinary subtraction operation, and for borrowed bits, you need to do a complement operation.

For example, 4 bits 1h minus 11h, the result is 1110, 11h-111h=1100h, 111h-1111h=1000h, 1111h-11111h=overflow. Also, 1h-10h=1111h, 1h-100h=1101h, 1h-1000h=1001h... Therefore, try not to do subtraction operations in the programming process, but strive to do addition operations.

Hello, the specific rules of binary subtraction are related to the encoding of truth values, such as: original code, complement code, etc.

Now suppose that two numbers are unsigned integers and are always larger minus lesser. (Because unsigned numbers cannot represent negative numbers, they cannot be reduced from small).

The minus digit is inverted one by one, the last digit is added by 1, and then it can be added with the subtracted digit, and there is no need to consider the problem of borrowing.

Example 1: Subtracted: 110000 Subtraction: 010111 (aligned with subtracted).

Inversion of subsituation (i.e. 0 becomes 1, 1 becomes 0): 101000

Add 1:101001 to the last digit

Add to the subtracted number:

1011001 (discards the portion that exceeds the length of the subtraction).

Due to the fact that two non-negative numbers are subtracted, their values cannot be greater than both. That is, the length cannot exceed the subtracted number, so the leftmost 1 is discarded.

Example 2: Subtracted: 11 (decimal 3), Subtracted: 10 (decimal 2);

The subtraction is reversed and added to 1:01+1=10 (it changes back).

Add: +10

101 (rounding off the leftmost 1 is the correct answer 01).

If there is no borrowing at a glance, you can directly reduce it. It's a problem to add 1 to the counter.

Example 3: Subtraction: 11001010 (decimal 202), subtraction: 00001001 (decimal 9).

Subtraction is taken and added by one: 11110111

Add: +11110111

111000001 (rounding off the leftmost 1 is the correct answer: 11000001).

Addition: 0+0=0;0+1=1；1+0=1；1+1=10；0 is 1. Subtraction: 0 0 = 0, 1 0 = 1, 1 1 = 0, 0 1 = 1.

When the binary number is converted to the ** system, the decimal point is taken as the starting point, and the left and right directions are segmented respectively, and each two digits are a paragraph, and the less than two digits are added to the left or right respectively.

Binary numbers. Convert to octal number: starting from the decimal point, the integer part is to the left, the decimal part is to the right, every 3 digits is a group of numbers represented by a decimal number of Wei He Kai, and less than 3 digits should be filled with "0" to make up 3 digits, and you have to hail to an octal number.

Binary numbers are converted to hexadecimal numbers.

When converting binary numbers to hexadecimal numbers, you only need to start from the decimal point, divide every four digits of binary to the left or right (less than four digits can be filled with 0), and then write the hexadecimal number corresponding to each group of binary numbers.