Abstract: An apparatus for identifying a pop-top can having a pull-tab activated opening member is comprised of a label, an adhesive backing and identifying indicia. The label is sized and shaped such that it has two generally circular sections joined by a neck. The circular sections fit the contour of the free end of the pull-tab. The neck and the circular sections are shaped to allow the label to become affixed to the pull-tab by the mating of the adhesive surfaces of each circular section to each other through an opening in the pull-tab. The identifying indicia, which may be a colored surface or typographical characters, distinguish one apparatus from another. A pop-top can is identified by affixing an apparatus to the pull-tab of the can.

Abstract: For most `natural` signals like audio and video, the first derivative with respect to time (or spatially as in video) can have a significant amount of error and still be perceived as accurate due to the masking properties of the ears and eyes. A Logarithmic Differential Compression (LDC) data stream representation of the first derivative is formed with four or less bits of mantissa and can be treated as both a logarithmic numeric representation and a floating point numeric representation without correction. A digital signal processor 524 is described which performs multiplication of LDC data with a simple scalar adder 600 and addition of LDC data with a simple four or less bit floating point adder 610. A digital signal processor is optimized to process LDC data and low cost arrays of these digital signal processors are formed to provide high performance systems for transforms and filtering.

Abstract: A method converts an n-bit floating point number to a logarithmic representation, the number having a first set of bits assigned to a mantissa, and a second set of bits assigned to an exponent. The logarithmic representation has a characteristic and a fraction. The method: (a) sets the characteristic of the logarithm equal to the second set of bits; (b) selects from a logarithm table a first logarithm of a first subset of the first set; (c) selects from the logarithm table a slope of a logarithmic function at the first logarithm; (d) multiplies the slope times a second subset of the first set to obtain an interpolated value; (e) adds the interpolated value to the first logarithm to obtain the fraction; and (f) adds the characteristic and the fraction to obtain the logarithmic representation.