Let a = 1.0 × 2 , b = −1.0 × 2 and c = 1.0 × 2 . Using the simple floating-point model described in the text (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit for the number), perform the following calculations, paying close attention to the order of operations. What can you say about the algebraic properties of floating-point arithmetic in our finite model? Do you think this algebraic anomaly holds under multiplication as well as addition?

b + (a +

c) =

b +

a) + c =