Data Representation — common mistakes

When asked to perform two's complement conversion, always state the number of bits you are working with (e.g., 'in 8-bit two's complement'). A common mistake is to forget to pad the positive binary number with leading zeros to the required bit length before inverting.

For convenience and readability. A long binary string like 1101010011101011 is difficult for a programmer to read, type, or remember. The same value in hexadecimal is D4EB, which is much shorter and less prone to transcription errors. It acts as a useful shorthand.

An unsigned integer uses all its bits to represent the magnitude of a positive number. An 8-bit unsigned integer can represent values from 0 to 255. A signed integer uses one of its bits (the MSB) to indicate the sign (positive or negative), so it can represent both positive and negative values, but over a different range. An 8-bit signed integer (using two's complement) represents values from -128 to +127.

You must know the context! If you are told it's an 8-bit unsigned integer, it represents 128 + 8 + 4 + 1 = 141. If you are told it's an 8-bit signed integer using two's complement, the leading '1' means it's negative. To find its value, you would perform the two's complement operation on it to find its positive magnitude.