Please write the details of your question here.
I don't know why 0b10000000 becomes 128 in an 8bit environment with a sign.
−127 = 0b10000001
0b100000000 (128) 0b01111111 (127) = 0b10000001 (127)
1 is
0b100000000 (128) 0b00000001 (1) = 0b11111111 (1)
I understand that.
That is, 127 to 127
It can be expressed by 0b10000001 to 0b11111111.
But I don't understand why 0b10000000 is 128.
0b100000000 (128)0b100000000 (128) = 0b000000000 (128 ??)
128 ≠ 0b10000000 is not.
Instead of calculating by calculation like this
If 128 is expressed by 0b10000000, it will be possible to make effective use of bits (because the value that can be expressed by one increases).
In an 8bit environment, when signed
Is it okay to recognize that I "decided" to express 128 as 0b10000000?
Supplementary information (FW/tool version, etc.)
Fundamental Information Technology Engineer Examination Nary question

Answer # 1

Answer # 2
It ’s a simple two's complement representation.
If you subtract 1 from 127, it's 128.What do you know about this?

Answer # 3
All bits are written here. Can you understand if you look at the list?
List of 8bit signed integers signed integer 
Answer # 4
Negative numbers can be thought of as follows.
For example, if you add a number X to 127 and it becomes 0, you can think of X as 127.
When representing a number with 8 bits (ignoring numbers over 8 bits). It will be as follows.0b0111'1111 (127) + X = 0b0000'0000 (0) ⇒ X = 0b1000'0001 (127)
Similarly,
0b0111'1110 (126) + X = 0b0000'0000 (0) ⇒ X = 0b1000'0010 (126)
...
0b0000'0001 (1) + X = 0b0000'0000 (0) ⇒ X = 0b1111'1111 (1)For 128
0b1000'0000 (128) + X = 0b0000'0000 (0) ⇒ X = 0b1000'0000 (128)I'm adding the same thing, so it feels a little strange. I don't think the idea is wrong.
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I don't know what the calculation is.
0b1_0000_0000 is 256 instead of 128, 128127 is not 127 and 1281 is not 1.
Similarly, 0b1_0000_0000 is 256 instead of 128.
I don't know what you want to calculate, but if you set the first "128" to 0b1_0000_0000 (256) as above and the next "128" to 0b1000_0000, which is 128 correctly, wouldn't it be the result you want?