Your computer uses 8 bits to represent decimal numbers (0, 1, 2, 3 and so on) in binary. What is the SMALLEST number for which an overflow error occur?

256

Explanation:

The largest number that can be represented using 8 bits (8 positions of binary 1 or 0) is 255.  This is assuming that the 8 bits are being used to represent only positive integer values.  In 8-bit binary, the decimal number is represented as 11111111.  This means that if you have an 8-bit integer variable with a decimal value of 255 stored in it (again, 11111111 in binary) and you attempt to add 1 more to it (255 + 1), the answer is 256.  256 would require a 9th bit of storage to represent it (100000000 in 9-bit binary) properly, and since the number is limited to 8 bits of storage, the system will throw an overflow error.  Overflow errors happen when you try to store a number in variable that is too small to hold the value.

Fun Fact: most modern computers use 64-bit system architecture.  This means that the largest number you can put into a single 64-bit integer variable is 9,007,199,254,740,992.  Adding 1 to that would, as you've probably guessed, cause an overflow error.

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