Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.

Image recorder having more than one recording head and image recording system containing the image recorder

Abstract: A control part comprises a division location setting part for setting a division location based on an image data; a scan start position setting part for setting scan start positions of recording heads based on the division location; an image data division part for dividing an image data by the division location; and a head movement control part for controlling movement of the recording heads. The division location setting part sets a division location in a blank area having no pixel to be recorded in the primary scanning direction, in the case of publication printing, in a center margin area between page data. Since the recording heads perform scanning concurrently their respective areas that are divided by the division location, no deterioration in image continuity occurs between the recording heads. This permits an image recorder, though having plural recording heads, capable of performing concurrent recordings without loss of continuity.

Arithmetic Operations in a Binary Computer

Abstract: The application of binary arithmetic in the computing circuits of a high speed digital computer is discussed in detail. The discussion covers, with numerous examples, the use of complements to represent negative numbers, the corrections necessary in the multiplication process as a result of the use of complements, and additional modifications of the process to simplify mechanization. A special division method well‐adapted to automatic computer use is described, and round‐off procedures are noted briefly. The article is concluded with a discussion of the storage of negative numbers as absolute values with a sign rather than in complement form.

Analysis of higher order pitch division for sub-32nm lithography

Abstract: The three knobs of optical lithography, namely process factor k1, wavelength (λ) and numerical aperture (NA) have been constantly pushed to print smaller features. To get an equivalent k1 value below the fundamental limit of 0.25, double patterning (DP) has recently emerged as a viable solution for the 32nm lithography node. Various DP techniques exist such as litho-etch-litho-etch (LELE), litho-freeze-litho-freeze (LFLF) and self-aligned sidewall spacer. In this paper, the potential of higher order pitch division (pitch/N, N>2) for sub-32nm lithography is analyzed. Compared to double patterning, higher order pitch division lithography offers higher resolution but also faces significant challenges such as added cost and tighter process control. Several process schemes are proposed and compared in terms of complexity, susceptibility to alignment error and CD uniformity control. It is shown that the overlay budget does not necessarily decrease compared to double patterning. The main challenge in higher order pitch division comes from controlling the key processing steps that directly form lines or spaces. In addition, line CD control is easier than space (gap) control in all four "positive-tone" processes studied, similar to the double patterning case. Among the proposed processes, a freezing assisted double spacer (FADS) process that is simpler than the common sidewall spacer approach shows promise for balanced process control.