Binary complement

I just came across a problem , seek b Value

byte b = (byte)129;

Just got the question , Let's take a look. , Ah , Isn't this forced type conversion ？byte It's symbolic , So we began to calculate ：

byte A byte , That is to say 8 Bit binary that 129 Namely ：10000001

At first glance, it is symbolic , That is, the sign bit remains unchanged , Other positions are inverted +1:11111110+1=11111111=-127（1+2+4+8+16+32+64）

balabala~ It's been a long time , Half an hour passed , So is there a better way ？

We know ,byte Is a signed single byte integer , So the range of stored numbers is [-128·127], Complement should be calculated as above . But why should we calculate like this ？

Because scientists define numbers as a ring , The largest number is followed by the smallest , In this way, we can [0·255] Assigned to [-128·127].
The bottom layer is the concept of complement .

So let's count ,129 Greater than byte Express the largest integer 127. And it's a ring , That's it 127 After that is byte The smallest negative number -128,-127 . OK, it's -127 了 , That's it . Is it a matter of minutes ？