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Computation of Differences

IP.com Disclosure Number: IPCOM000081478D
Original Publication Date: 1974-Jun-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 4 page(s) / 87K

Publishing Venue

IBM

Related People

Riso, V: AUTHOR

Abstract

The value of any number Z(i) written in 2's complement code is derived from the following equation: (Image Omitted) where M is the number of bits per word Z(i), and any Z representing the k/th/ bit of Z(i) starting from the lowest order, i.e., order one.

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Computation of Differences

The value of any number Z(i) written in 2's complement code is derived from the following equation:

(Image Omitted)

where M is the number of bits per word Z(i), and any Z representing the k/th/ bit of Z(i) starting from the lowest order, i.e., order one.

By taking into account the logical identity 1 = Z/k/(i) + Z/k/(i) and by substituting the bit Z/M/(i) for any bit Z/M/(i), it is possible to derive an equation
(2) from (1):

(Image Omitted)

in which Z/0/(i) is an extra bit, or flag, always equal to 0 and forced into the bit stream belonging to Z(i).

Now, assume it is desired to compute a sum Y(i) of n productsd alpha(i).Z(i), where alpha(i) are fixed binary words coded in 2's complement code, a are complement code and available in series by bit.

(Image Omitted)

All possible values of S(j) needed to compute Y(i), as well as S(0), mey be stored into a read-only memory (ROM) as soon as the fixed values for alpha(i) are defined. Then any Y(i) may be computed by accumulating values of S(j) fetched out of that ROM, by using as addressing information the words Z/j/(1) Z/j/(2) Z/j/(3) ... Z/j/(m) with j = 1, 2, 3, ..., M, varying at bit rate.

As shown in the figure, each word Z(1) to Z(n) is fed in series to one out of n input lines. These lines are XORed with a logic input G and provide, at each bit time, n output bits on n output lines. Each output line may be individually XORed with one of n logic signals G(1) to G(n) (the purpose of which will be described below). The outputs of XOR(1) XOR(n) are used as an addressing word that fetches out of ROM a value of S(j), which is then fed into an accumulator (ACCU).

In operation, a Y(i) value is computed as follows. Star...