Final answer:
The 2's complement signed binary number 100000000 represents the negative decimal value -256.
Step-by-step explanation:
The 2's complement signed binary number 100000000 represents a negative value in decimal. To determine the decimal value, we first note that the leftmost bit is 1, which indicates a negative number. The remaining bits would normally represent the magnitude of the number in binary.
But since this is a 2's complement representation, we must reverse the process to find the original positive value before it was negated. First, we invert all the bits of 100000000, except for the leading 1, which gives us 011111111. Then we add 1 to this binary number.
However, adding 1 to 011111111 would result in 100000000 again because of binary carry over, which is our original number. Therefore, we can conclude that our number, 100000000, in 2's complement, is -1*(28). Hence, the decimal value is -256.