Sign-magnitude is probably the simplest of the binary representations. To get the negative binary representation of a negative number, just take the positive number and set the sign bit.
81 is 01010001, so -81 is 11010001. 127 is the largest possible value in a signed 8-bit type, so try the first seven bits 1 and the last bit (the sign bit) 0: 01111111. -127 would simply be the same thing with the sign bit set: 11111111.