A fixed number of bits can only hold so many values. Past the top, the count wraps around to the bottom, and that wrap is a bug that no error message reports.
About 2 min of reading
Probe the wrap at a width.
Add one past the top of a byte.
Before you run it, say out loud what it will print. Then open the answer.
Subtract one below zero.
Before you run it, say out loud what it will print. Then open the answer.
Store three hundred in a byte.
Before you run it, say out loud what it will print. Then open the answer.
Print what thirty two bits hold.
Before you run it, say out loud what it will print. Then open the answer.
Read the first example one line at a time. A line that prints shows what appears on screen; the rest set things up quietly.
Overflow does not raise in most languages. The program keeps running with a wrong number, which is why it reaches production so often.
A format states its width, and a value that does not fit is a contract violation. Catching it at the edge is the fix, not reading a wrong number.
print((255 + 1) % 256)One past the top of a byte is zero. The row of bits has nowhere to carry, so it starts over.
print((0 - 1) % 256)One below zero is the top. The row rolls the other way, which is the same rule in reverse.
n = 255
n = (n + 1) % 256
print(n)A byte-sized counter goes back to zero. A score that resets at 256 is this exact bug.
print(2 ** 32)Thirty two bits hold four billion values. The wrap is still there, it is just far away and easy to forget.
print((200 + 100) % 256)Three hundred stored in a byte is forty four. Nothing crashed, the number is simply wrong.
a, b = 200, 100
print(a + b > 255)Checking the result against the width is how a wrap is caught. The check has to be written on purpose.
print(2 ** 8, 2 ** 16, 2 ** 32)Widths are picked to fit the biggest expected value with room left over. Too small and it wraps.
print(2 ** 64)A wider row holds more values and takes more bytes. Choosing a width is trading memory against the risk of a wrap.
Each one is defined here on this site. Open the entry for the full definition and the other words it points at.