Abstract: A method of generating electronic monetary tokens that supports off-line transactions while preventing double-spending. Generation of electronic token halves by a financial services provider begins in response to a request from a buyer to generate electronic monetary tokens to be used with an identified seller. First, the financial services provider generates a multiplicity of electronic monetary tokens. Second, the provider splits each electronic monetary token into two electronic token halves and associates with each the same serial number. These electronic token halves when combined recreate the electronic monetary token from which they were generated, but by themselves neither electronic token half has any value. Nor can either electronic half by itself be used to create the electronic monetary token without the token half's mate.

Abstract: A system for generating images having display based computation. The system of the present invention divides the image generation process between the display and a host computer system. The computation element of the display includes rendering mesh comprising a plurality of processing elements. One or more processing elements of the rendering mesh correspond to one or more pixels of the display. The host computer system includes a processing means for generating a rendering mesh map. The rendering mesh map is used to identify processing elements of the rendering mesh which will receive "seed" pixel values. The rendering mesh map is stored in a rendering mesh map buffer. The "seed" pixel values are stored in a frame buffer and represent an original rendering of an image. When the rendering mesh is seeded, pixel values are determined for the "unseeded" processing elements.

Abstract: In order to correct for keystoning distortion when projecting a transparency onto a projection screen, computer software is used to deliberately distort an electronic image. A transparency, which can be a slide or a projection panel display such as an LCD panel, is then produced with the intentionally distorted image. The oblique angle between the horizontal plane through the projector and the viewing screen is compensated for by an inverse tapered compression of the electronic image. In one embodiment, a test slide is generated with a plurality of non parallel line pairs, each line pair representing a different distortion correction to an image. The test slide is projected to the screen to be used. A pair of line pairs most parallel to each other is identified. The line pair identification is used to activate the portion of software which generates that particular image distortion.

Abstract: Apparatus for performing high-speed, parallel multiplication in a data processing system wherein each multiplication requires only one step to reduce a plurality of summands to two numbers whose summation equals the product. The fractional portion of two floating point numbers, the multiplier and the multiplicand, are coupled to registers. Thereafter, the multiplicand is multiplied by segments of the multiplier and the resultant products are summed together using a conventional shift and add means. The multiplicand and a segment of the multiplier are each coupled to a plurality of multiplier circuits which produce a plurality of summands. These summands are coupled to a plurality of counter circuits in a manner such that the digits of all of the summands representing the same power of the number 2 may be counted.