Final answer:
Two's complement is a method for representing negative binary numbers where the Most Significant Bit (MSB) indicates the sign of the number and also contributes to its magnitude. The MSB is 0 for positive numbers and 1 for negative numbers. To find the two's complement of a binary number, invert all bits and add 1 to the result.
Step-by-step explanation:
Two's complement is a mathematical operation on binary numbers, as well as a binary signed number representation based on this operation. Its widespread use is due to the ease of performing arithmetic with digital circuits. In two's complement, the Most Significant Bit (MSB) has two roles. Firstly, it indicates the sign of the number: a 0 in the MSB represents a positive number, and a 1 represents a negative number. Secondly, it contributes to the magnitude of the number when determining the actual value the binary represents. However, for negative numbers in two's complement, the values of the bits are inverted and 1 is added to the resulting number to find its positive counterpart.
For example, in an 8-bit system, the binary number 00001010 represents the decimal number 10. Its MSB (the leftmost bit) is 0, indicating it is positive. To represent -10, we invert the bits (11110101) and add 1, resulting in 11110110 in two's complement form. Here, the MSB is 1, indicating the number is negative.