# Logic Design for Array-Based Circuits

### by Donnamaie E. White

Copyright © 1996, 2001, 2002 Donnamaie E. White

# Faults and Fault Detection

Last Edit July 22, 2001

## Case Study - 16:1 MUX D Flip/Flop Circuit

### 100% FAULT-GRADE VECTOR SET

The following circuit was developed as a teaching circuit and as such has parameters and labels beyond what would appear in an actual circuit schematic. These parameters have nothing to do with the required Functional, AC Test or Parametric Vector sets.

A parametric gate-tree, used for VIH and VIL measurement is included and its output signal is listed. A simulation format requires that all I/O signals and internal enable nets be listed.

The test sequence for a 16:1 MUX 'was altered to allow clocking to occur between vector steps. The rule of one input per vector changing state is honored in that data and clock do not change in the same vector. The sequence begins after the circuit RESET is executed.

Both the schematic set and a formatted (compacted) output vector set is shown here. The output vectors include input, output and enable signals.

### The Marquand Map

The Marquand Map for logical analysis was proposed in a mathematical paper in the late 1800's. It is a convenient mapping method for large functions. The Karnough Map was developed in the 1950's specifically for 4-variable circuits (for coding) and is messier to use in these cases. Figure 9-10 through Figure 9-13 show different sizes of Marquand Maps with minterms labeled.

Figure 9-10 2-Input 1-Output Marquand Map

Figure 9-11 3-Input 1-Output Marquand Map

Figure 9-12 4-Input 1-Output Marquand Map

Figure 9-13 5-Input 1-Output Marquand Map (Split)

Copyright @ 2001, 2002 Donnamaie E. White, White Enterprises
For problems or questions on these pages, contact dew@Donnamaie.com