Why is the range of values that can be stored in a byte primitive -128 to 127?

Question

I know the range, but can someone please explain it to me with a little detail?

Answer 1

You have seven bits plus a sign-bit available to express those 256 numbers as signed integers.

Positive numbers would be 0 to +127, which are 128 values with the sign bit set to zero as a "positive indicator."

Negative ones are 0 to -127, which are 128 values with the sign bit set to one as a "negative-indicator."

Answer 2

It's been a while, so I might be a bit fuzzy, but:

You are talking about a signed integer where the first bit indicates if it is positive or negative (0=positive, 1=negative). If it is positive, you use the rest of the 7 bits like you would normally count in binary, if it is negative I believe you subtract 255 or (2^n-1) from the value.

So,

0111 1111 = 127
1111 1111 = 127-255= -128