A.2.2.2 Logic Blocks

The series connection of two NMOS switches controlled by the voltages A and B is conducting only when both A and B are HIGH. Thus, the series connection implements the logical AND function, or, the Boolean product

$$P(A,B) = AB .$$ (A.19)

Likewise, a parallel connection of two NMOS switches implements the logical OR function, or, the Boolean sum

$$S(A,B) = A+B .$$ (A.20)

Furthermore, such logical functions can again be combined by series and parallel connection. This way any boolean expression of a vector of variables and their complements can be constructed. The complements $\overline{x_i}$ of the variables x_i can be built with inverters. An example is shown in Fig. A.7, where a more complex function F is implemented with a block of NMOS transistors (note that the function type of such a block is conduction, not voltage). The dual block^A.1 of PMOS transistors implements the complementary switching function $\overline{F}$, i.e., the dual p-block is conducting exactly when the n-block is not. Now, a complete CMOS gate can be built by simply connecting the p-block from to the output and the n-block from the output to ground, like in Fig. A.8, so that the output voltage is the complement of the switching function of the n-block: $Y = \overline{F}$

Figure A.7: N-block implementation of a Boolean function

[Circuit]

[Boolean switching function]

F = AB(C+D)

Note, that an n-block must always have a connection to ground (possibly through other NMOS transistors) because $\ensuremath{V_{\mathit{GS}}}\xspace -\ensuremath{V_{\mathit{T}}}\xspace$ must be sufficiently large and positive to turn the transistors on. For the same reason a p-block must always have a connection to . This is one reason why the use of NMOS and PMOS transistors in the same logic block is unfavorable.

Figure A.8: CMOS gate built from an n-block and the dual p-block

[Circuit]

[Boolean function]

$Y = \overline{AB(C+D)}$

Footnotes

... block^A.1

A logic block can represented as a graph where each edge corresponds to a switch. The dual block is constructed by taking the dual graph, i.e., by replacing series connections with parallel connections and vice versa.