Hi,
Well, the bigest number that you can represent whith 8 bits is ( 2 ^ 8 ) - 1 = 255.
In 2's complement, you can represent numbers form -2 ^ ( 8 - 1 ) = -128 to +( 2 ^ ( 8 - 1 ) - 1 ) = +127.
127 - (-128) = 255 !!
Well, when you multiply the 2 numbers you can multiply:
- a positive number by positive number;
- a negative number by negative number;
- a positive number by negative number.
The bigest positive number that you can represent is : +127.
The bigest negative number that you can represent is : -128.
If you multiply the bigest positive number by himself:
(+127) * (+127) = +16'129
If you multiply the bigest negative number by himself:
(-128) * (-128) = +16'384
If you multiply the bigest negative number by the bigest positive number:
(-128) * (+127) = -16'256
Conclusion:
(*) The bigest number you have is +16'384;
(*) The smallest number you have is -16'256;
regards.