Fault Detection in Digital Circuits 21 Figure 2.6: Singular cubes for the two-input NOR function. The propagation of a gate are those that cause the output of the gate to depend only D-cubes on one or more of its specified inputs. Thus, a fault on a specified input is propagated to the output. The propagation for a two-input NAND gate are: D-cubes a b f 1 D D D 1 D D D D The propagation 1DD and indicate that if one of the inputs of the NAND gate is 1, D-cubes D1D the output is the complement of the other. propagates multiple input changes through the DDD NAND gate. Propagation of a gate can be constructed by intersecting its singular cubes D-cubes with output values. The intersection rules are as follows: 0 0 = 0 = 0 = 0 x x ∩ ∩ ∩ 1 1 = 1 x = x 1 = 1 ∩ ∩ ∩ = x ∩ x x 1 0 = ∩ D 0 1 = ∩ D For example, the propagation of a three-input NOR gate can be formed as shown in D-cube Figure 2.7.
Fault Detection in Digital Circuits 21 Figure 2.6: Singular cubes for the two-input NOR function. The propagation D-cubes of a gate are those that cause the output of the gate to depend only on one or more of its specified inputs. Thus, a fault on a specified input is propagated to the output. The propagation D-cubes for a two-input NAND gate are: a b f 1 D D D 1 D D D D The propagation D-cubes 1DD and D1D indicate that if one of the inputs of the NAND gate is 1, the output is the complement of the other. DDD propagates multiple input changes through the NAND gate. Propagation D-cubes of a gate can be constructed by intersecting its singular cubes with output values. The intersection rules are as follows: 0 ∩ 0 = 0 ∩ x = x ∩ 0 = 0 1 ∩ 1 = 1 ∩ x = x ∩ 1 = 1 x ∩ x = x 1 ∩ 0 = D 0 ∩ 1 = D For example, the propagation D-cube of a three-input NOR gate can be formed as shown in Figure 2.7.
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