Graphics and imaging are important in scientific, academic and industrial environments. In the past graphics systems have been used with large computers and were only available to a minority of users. The relatively small and specialized use of graphics has inhibited sharing of software and prevented standardization necessary for widespread use. Dense semiconductor memory has recently become easily available in large quantities and makes high resolution graphics and imaging systems feasible. The concepts leading to the design of the present system come from the need to provide a large number of graphic and imaging functions, in a compact form, to a commonly used microprocessor bus. Three fundamental functions are implemented: a video frame digitizer, an image memory, and an output video generator. Video images can be digitized in one frame time with a precision of 1, 2 or 4 bits per pixel. The video generator can display the images in gray levels or in color. The software selectable system parameters include a variety of image formats, video output controls, digitization commands, addressing modes, vertical image offset, and lightpen controls. A novel contouring digitization mode is useful to reduce images obtained in gray scale to outline form. Such real-time preprocessing reduces memory and bandwidth requirements. Photographic illustrations demonstrate various operating modes.

Given a minimal sequential machine M and a positive integer T , it is desired to partition the state set of M into T classes, say S 0 , S 1 , · · ·, S T -1 , such that all states in S 1, under all possible inputs, pass into states in S i +1 (mod T ) . If such a T -partition exists, M can be realized by means of periodically-varying logic, which often results in the saving of memory elements. The period of M is defined as the greatest common divisor of all cycle lengths of M —a quantity which can be readily evaluated since it depends only on a finite set of independent loops exhibited by the state graph. The main result is that a T -partition exists for M if and only if T is a divisor of the period of M . For every such T , an algorithm is given for constructing the corresponding partition. If M is not required to be minimal, it is shown (constructively) that a T -partition exists for every T .