8-bit 2's complement numbers are a way of representing signed integers in binary form. They use 8 bits (1 byte) to represent a number, with the leftmost bit being the sign bit. A 0 in the sign bit represents a positive number, while a 1 represents a negative number. This method of representation allows for both positive and negative numbers to be represented using the same number of bits.
To add two 8-bit 2's complement numbers, you simply add the two numbers together using the same method as binary addition. If the result is greater than 8 bits, the extra bit is dropped and the result is considered to have overflowed. This overflow can result in an incorrect answer.
Overflow occurs when the result of adding two 8-bit 2's complement numbers is too large to be represented by 8 bits. This can happen when adding two positive numbers, two negative numbers, or a positive and a negative number. Overflow is an indication that the result is incorrect and needs to be adjusted.
Overflow is indicated when the result of adding two 8-bit 2's complement numbers is either greater than 127 or less than -128, as these are the maximum and minimum values that can be represented with 8 bits. To indicate overflow, the carry bit (the leftmost bit that was dropped) is used. If the carry bit is 1, it means that the result has overflowed and the answer is incorrect.
Yes, addition with 8-bit 2's complement numbers can produce an incorrect answer if there is overflow. This can happen when adding two numbers with the same sign (both positive or both negative) that result in a number larger than 127 or smaller than -128. In these cases, the carry bit will be 1, indicating that the result has overflowed and is incorrect.