The Representation of Numbers in Computing Systems

The chapter contains fundamental notions referring to the number representations in computation, in fixed point and in floating point. As regards the fixed point, in distinct sections we analyze the binary numbers and decimal numbers representations. We present, together with their advantages and disadvantages, the representations of fixed point binary numbers in sign-magnitude, ones complement and twos complement codes, in particular aiming toward the addition operation. Referring to the floating point representations, the emphasis is on the issues concerning the biased representation of the exponent and the normalized representation of the mantissa. Moreover, the specific elements corresponding to the IEEE 754 floating point binary number representation standard are detailed.