Binary signed integers complement 100000000 represents a decimal number why 128 is not 0

Complement10000000, how big does it mean?

This eight-digit complement represents: 128.

This problem cannot be solved with the original code.

Because, 128, there is an eight-digit complement, but there is no eight-digit original code sumReverse code

The definitions of both the original code and the reverse code are flawed:

A number zero, but they both define two encodings +0 0!

Therefore, the eight-digit original code is reversed, which can only represent 127 127.

128 cannot be represented.

Therefore, finding the complement of 0 or 128 with "take and add one" will not work.

Similarly, using "take and add one" to find the original code corresponding to the complement code 1000 0000 is also not effective.

The formal way to find the complement is to use the definitive:

When x > = 0, [x ] complement = x; Zeros and positive numbers do not need to be transformed.

When x < 0, [x] complement = x + 2 n. n is the number of bits of the complement.

This definition is universal. You can find it in the book.

Then, [ 128] complement = 128 + 2 8 = 1000 0000 (binary.)

So, the eight-digit complement 1000 0000 represents the value 128.

The first step of the complement is 1, which is definitely a negative number.

The remaining 7 zeros are inverted by digit and added by 1

is 128, so consider that the sign bit is.

－128。

This number is quite special, so let's write it down.

Take a look:

I think 128 may be wrong.

I think it's +0

It's 101100.

The complement of a negative number is a digit negation of its original code, except for the sign bits; Then add 1 to the whole number.

1000110 negation of each bit, except for the sign bit, -0111001.

Add 1 to the whole number to get -0111010.

Turn the minus sign into 1 and the complement of -1000110 is: 10111010.

Binary numbers have two characteristics: they are composed of two basic characters, 0,1, and the law of binary number operation is every two to one.

In order to distinguish it from other decimal numbers, binary numbers are usually written with a base number 2 at the bottom right of the number, or a b after the addition of a number.

For example, a binary number 10110011 can be written as (10110011)2, or 10110011b, or unmarked for decimal numbers. The data in the computer is represented by binary numbers because binary numbers have the following characteristics:

1) There are only two characters 0 and 1 in a binary number, which represent components with two different steady states. For example, there is no current in the circuit, and the current is represented by 1, and the absence of current is represented by 0. Similarly, the voltage in the circuit is high and low, and the transistor conduction and cut-off.

2) Binary number operation is simple, which greatly simplifies the structure of the arithmetic parts in the calculation.

Computer signed machine number theory fixed-point method representation and floating-point method representation have three representations: original code, inverse code and complement original code: the original code notation form is the same as the original binary number representation method, only the original code is increased.

What is the complement of the binary number 110 1010?

The eight-digit complement of the binary number 110 1010 is: 1001 0110.

The 11101001 binary number, if it is an unsigned number, its decimal value is 233; If it is a signed number represented by a complement, its decimal value is -105.

Binary numbers have only two basic symbols, "0" and "1", which are easy to represent by two opposing physical states. For example, available"1"Indicates the "closed" state of the light switch, and "0" indicates the "off" state.

The turn-on of the transistor represents "1" and the cut-off represents "0"; All devices with two opposing steady states, such as the charging and discharging of capacitors, the presence and absence of electrical pulses, the positive and negative polarity of pulses, and the high and low potentials, can represent binary "0" and "1".

Complement means in addition to one sign bit, the first sign bit, 0 means positive, positive complement and the original code are the same, 1 means negative, the original code is inverted, add 1, the sign bit remains unchanged.

Range: -127---127

8-bit binary number with sign, back can represent a total of 2 A 8 (256) numbers, the first bit is the sign bit, because the sign bit 0 represents a positive number, 1 represents a negative number, so the smallest number is 10000000 (-128), and the largest number is 01111111 (127).

With an eight-digit complement binary, the decimal number can be represented: 128 127.

2. What is the decimal number represented by the signed integer (complement) 1000 0000?

It's 128. The oft-said "take the counter plus one" will not solve this problem.

Because, in the eight-digit original code and the reverse code, "128" cannot be represented.

You must use the simplest conversion formula to find 128.

And what is written in the textbook is that "the original code of the trapped sensitive symbol bit is cracked, the reverse code is taken and the symbol bit is added to the same", which is to sincerely add confusion.

The original code of the negative integer 0, sign bit 1, other bits 0 --10000000 (assuming a total of 8 bits, the highest bit is the sign bit).

The inverse code of the negative integer jujube ruler 0, the sign bit remains unchanged, which is 1, and the other bits 0 becomes 1,--11111111

The complement of a negative integer 0 is equal to its inverse plus 1 --

The 1 in square Kuanpei's parentheses is automatically lost due to overflow, becoming a stool height 00000000, so the complement of the positive integer 0 and the negative integer 0 is the same, 00000000

The original code of the negative integer 0, sign bit 1, other bits 0 --10000000 (assuming a total of 8 bits, the highest bit is the sign bit).

The inverse of a negative integer 0, the sign bit remains unchanged as 1, and the other bits 0 become 1 ,--11111111

The complement of a negative integer 0 is equal to its inverse plus 1 --

11111111 + 1 = [1]000000000 The 1 in square brackets is automatically lost due to overflow and becomes 000000000, so the complement of the positive integer 0 and the negative integer 0 is the same, 000000000

x represents the true value of the trapped remainder vertical (+, the fixed point number is large, the decimal point can be moved casually, and it can represent an integer, so I use a decimal number as an example, 10b, 1b represents a binary number).

x] complement = (2+x) mod2

i.e., if x is positive, (10b + mod 10b = so the positive complement is the same as the original.)

x if negative, (10b - 10b = 1.!.)x1!x2...xn+2^(-n))mod 10b=

1.!x1!x2.!xn +2^(-n)

Indicates non), so the negative complement is in addition to the sign bit to take the inverse last digit plus 1 because of the destruction of this = -

How much is binary 00001111-10101010 equal to, the result is represented by the binary return key delay code, which can be followed by the following bright blocking steps:

First invert the meiotic 10101010 to get 01010101

Then add 1 to the result of the inversion to get 01010110, which is the complement of the subtraction.

The subtraction 00001111 and the complement of the subtraction are then added 01010110 to get 01100101

Finally, determine whether the sign bit (highest digit) of the result is 1, if it is 1, it means that the result is negative, and you need to take the negative plus 1 again to get the complement; If it is 0, it means that the result of the leakage is positive, and the output can be done directly.

In this problem, the sign bit of the result is 0, so you don't need to add 1 again, just output 01100101.

Therefore, binary 00001111-10101010 is equal to 01100101.