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Unformatted text preview: ution with an AND gate at the output might have fewer
gates or gate inputs. A twolevel ORAND circuit corresponds
to a productofsums expression for the function. This can be
obtained from the 0′s on the Karnaugh map as follows: f ′ = c′d + ab′c′ + cd + a′b′c (73)
f = (c + d)(a′ + b + c)(c′ + d′)(a + b + c′) (74)
Equation (74) leads directly to a twolevel ORAND circuit. Figure 75 To get a threelevel circuit with an AND gate output, we
partially multiply out Equation (74) using (X + Y)(X + Z) = X +
Y Z:
f = [c + d(a′ + b)][c′ + d′(a + b)] (75)
Equation (75) would require four levels of gates to realize;
however, if we multiply out d′(a + b) and d(a′ + b), we get f = (c + a′d + bd)(c′ + ad′ + bd′) (76)
which leads directly to a threelevel ANDORAND circuit. Section 7.1 (p. 194)
Figure 76 This example: best twolevel solution had an AND gate at
output, bes...
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This document was uploaded on 03/16/2014 for the course EE 316 at University of Texas at Austin.
 Spring '08
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