VLSI Digital Signal Processing Systems: Design and Implementation

14.6    DATA FORMAT CONVERSION

In this section, conversion from nonredundant to redundant and vice-versa are presented for both radix-2 and radix-4 representations.

Fig. 14.17    Nonredundant to redundant radix-2 conversion for wordlength 4.

Fig. 14.18    Nonredundant to maximally redundant radix-4 conversion for wordlength 4.

14.6.1    Nonredundant to Redundant Conversion

This conversion process is relatively easy as the nonredundant input digit set is a subset of the redundant input digit set.

14.6.1.1    Radix-2 Representation

Let the nonredundant number X be denoted by X = x₃ . x₂ x₁ x₀, and the corresponding redundant representation be denoted by Y = y₃ . y₂ y₁ y₀ where each digit y_i is encoded as – and each digit x_i represents a 1 or 0. Note that the bit x₃ has a weight –1 in two’s complement number system. This conversion is shown in Fig. 14.17.

14.6.1.2    Radix-4 Representation

Consider the conversion of a radix-4 complement number, X , to a maximally redundant number, Y. The digits of X, x_i, are encoded using 2 wires according to and the digit y_i is encoded using Equating ...