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KEY TO PAGES 141-144

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Simplification of Logic Expressions:Derivation of Minimal Sums by Karnaugh Map.

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Derivation of Minimal Sums by Karnaugh Map Because of its pictorial nature, a Karnaugh map is a very powerful tool for deriving manually all prime implicants, irredundant disjunctive forms, minimal sums, and also absolute minimal sums. Algebraic concepts such as prime implicants and consensuses can be better understood on a map. One can derive all prime implicants, irredundant disjunctive forms, and minimal sums by the following procedures on Karnaugh maps, when the number of variables is small enough for the map to be manageable. Procedure 28.1: Derivation of Minimal Sums on a Karnaugh Map This procedure consists of three steps: 1. On a Karnaugh map, encircle all the 1-cells with rectangles (also squares as a special case), each of which consists of 2 i 1-cells, choosing i as large as possible, where i is a non-negative integer. Let us call these loops prime implicant loops , since they correspond to prime implicants in the case of the Karnaugh map for four or fewer variable...
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Dynamic Random Access Memory:DRAM Memory Cell

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DRAM Memory Cell In early CMOS DRAM storage cell design, three-transistor and four-transistor cells were used in 1-Kb and 4-Kb generations. Later, a particular one-transistor cell, as shown in Figure 55.4(a), became the industry standard [5,6]. The one-transistor (1T) cell achieves smaller cell size and low cost. The cell consists of an n-channel MOSFET and a storage capacitor C s. The charge is stored in the capacitor C s and the n-channel MOSFET functions as the access transistor. The gate of the n-channel MOSFET is connected to the word-line WL and its source/drain is connected to the bit-line. The bit-line has a capacity C BL , including the parasitic load of the connected circuits. The DRAM cell stores one bit of information as the charge on the cell storage capacitor C s. Typical values for the storage capacitor C s are 30 to 50 fF. When the cell stores “1”, the capacitor is charged to V DD – V t. When the stores “0”, the capacitor is discharged to 0 V. During the READ ...
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CMOS/BiCMOS Technology:BiCMOS Technology.

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BiCMOS Technology Development of BiCMOS technology began in the early 1980s. In general, bipolar devices are attractive because of their high speed, better gain, better driving capability, and low wide-band noise properties that allow high-quality analog performance. CMOS is particularly attractive for digital applications because of its low power and high packing density. Thus the combination would not only lead to the replacement and improvement of existing ICs but would also provide access to completely new circuits. Figure 2.25 shows a typical BiCMOS structure [112]. Generally, BiCMOS has vertical npn bipolar junction transistor, lateral pnp transistor, and CMOS on the same chip. Furthermore, if additional mask steps are allowed, passive devices are integrated, as described in the previous section. The main feature of the BiCMOS structure is the existence of a buried layer because bipolar processes require an epitaxial layer grown on a heavily doped n+ subcollector to reduce co...
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