+127 and the sign-bit boundary — two's complement
coreone more and it wraps
Answer
01111111
Why this example is worth doing
0111 1111 is the largest positive eight-bit value; adding one gives 1000 0000, which reads as −128. The page shows the wrap as an arithmetic fact rather than an error, and points out that the hardware does not know anything went wrong — the same bits are a perfectly good unsigned 128. Signedness is an interpretation the programmer supplies, not a property of the register.
Try your own input in the Two’s complement. Encode and decode signed binary at any width, with overflow and sign extension.
How the answer is reached
127 in 8-bit two's complement
Encode 127 in 8-bit two's complement. Representable range: -128 to 127.
127 in binary01111111— Non-negative values are plain binary, zero-padded to the width.
8-bit pattern0111 11110x7F
check01111111 reads 127 unsigned and 127 signed