Sign extension means that any given signed number can be represented with more bits by simply repeating the sign bit. For example, 0005 = +5 and 00005 = +5. This holds true for negative numbers as well. For example, 1011 = -5 and 11011 = -5. Also, 11111011 = -5. Using finite summation notation, prove that sign extension can be applied to any 2's complement binary integer, B, with b number of bits.