Which configuration yields a NOR function in ladder logic?

Which configuration yields a NOR function in ladder logic?

• A. Two XIO In Series
• B. Two XIC In Series
• C. Two XIO In Parallel
• D. Two XIC In Parallel

Answer: (A)

In ladder logic, placing two normally closed contacts in series creates an inverted path for each input and uses an AND relationship between them. A normally closed contact conducts only when its input is off, so the first contact is true when input A is off, and the second is true when input B is off. The rung will close (energize the output) only if both inputs are off, which is (NOT A) AND (NOT B). By De Morgan’s law, (NOT A) AND (NOT B) is equivalent to NOT (A OR B), which is NOR. So this configuration yields the NOR function: the output is true only when both inputs are false. If you mix in normally open contacts or place them in parallel, you’d get other logic functions such as AND, OR, or NAND, not NOR.

In ladder logic, placing two normally closed contacts in series creates an inverted path for each input and uses an AND relationship between them. A normally closed contact conducts only when its input is off, so the first contact is true when input A is off, and the second is true when input B is off. The rung will close (energize the output) only if both inputs are off, which is (NOT A) AND (NOT B). By De Morgan’s law, (NOT A) AND (NOT B) is equivalent to NOT (A OR B), which is NOR. So this configuration yields the NOR function: the output is true only when both inputs are false. If you mix in normally open contacts or place them in parallel, you’d get other logic functions such as AND, OR, or NAND, not NOR.