# Logic NOR Gate

- Muhammad Shahid
- m_shahid@live.co.uk
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### Logical NOR Gate

The logic NOR gate is the reverse or complement form of the logic OR gate which was discussed in the previous article. Similar to the logic NAND gate, it is a series combination of logic OR gate and an inverter thus forming a logic NOR gate. The logic NOR gate equivalent is shown in the following figure.

The logic NOR gate’s output becomes “HIGH” only when both of its inputs are at “LOW” states and for the rest of the states, the output will be in “LOW” level state. This is in exact contradiction to the logic function performed by the OR gate and because of this contradiction, it is called Not-OR (NOR).

In Boolean algebraic or logical expression, the logic NOR is a form of multiplication that is performed on the complements of the inputs. The expression of logic NOR is denoted by a plus (+) sign between the operands (inputs) and has an overline. Whereas, the overline represents an inversion of the logic OR. The expression for the two-inputs NOR gate is given below:

**Resistor-Transistor NOR Gate**

In the following figure, a basic two-input NOR gate constructed using Resistor-Transistor Logic (RTL) is shown.

When both inputs “A” and “B” are “LOW” then both transistors are in saturated “OFF” states and a state “HIGH” appears at the output (Q). Turning any of the inputs to logic “HIGH” will drive the relative transistor to the “ON” state and thus completing the path from VCC to Ground through a resistor (R). Which gives a state “LOW” at the output (Q).

**Logic NOR Gate Symbol & Truth Tables**

The representation of a NOR logic by a symbol is shown in the following figure. An inversion bubble at the output denotes the inversion of the multiplication.

The truth table of a two-input NOR logic gate is shown below:

Similarly, the truth table of a three-input NOR logic gate is as follow:

The Boolean expression can be extended to include multiple inputs to obtain NOR logic operation. However, commercially available NOR logic circuits have up to four inputs but the number of inputs can be further extended by cascading the NOR logic circuits. In the following figure, five two-inputs NOR gates are cascaded together to obtain a four-input NOR logic function.

The Boolean expression for this cascaded circuit can be written as:

**Odd Number of Inputs**

The NOR logic circuit having an odd number of inputs can be constructed by driving the unused input to logic “LOW” or ground through a pull-down resistor. This will ensure that another input(s) of the NOR logic gate is truly reflected at the output. It is explained in the following diagram where unused input is pulled down using a pull-down resistor.

### Universal Gate

Similar to the logic NAND gate, the logic **NOR gate** also exhibits the universal logic characteristics i.e. other logic gates can be constructed by forming the different combinations of logic NOR gates. Besides basic logic gates (AND, OR & OR), exclusive-OR and exclusive-NOR gates can also be constructed using universal gates. The examples of forming the AND, OR, and NOT logic by using NOR gates are shown in the following figure.

**Commercially Available NOR Gates**

The NOR logic gates are available in both TTL and CMOS logic families. The most commonly used NOR logic packages are:

**CMOS based NOR Gate IC Package**

- CD4001 Quad 2-input
- CD4025 Triple 3-input
- CD4002 Dual 4-inputs

**TTL based NOR Gate IC Package**

- 74LS02 Quad 2-input
- 74LS27 Triple 3-input
- 74LS260 Dual 4-input

**Example of NAND Logic**

In the following figure, a NOR gate is used to drive a 12V relay to switch on the lamp using NI Multisim. The NOR gate (74LS02) turns on the relay when all of the inputs are connected to Ground/ 0 V. The relay thus turns on the lamp through an external circuit of 12V. When any of the input is connected to VCC, NOR logic goes “OFF” turning the relay and lamp to “OFF” state.

**Conclusion**

- The output of the NOR logic is “HIGH” when all of the inputs are in logic “LOW” states.
- Any of the inputs in the logic “HIGH” state will drive NOR logic to the “OFF” state.
- The NOR logic gates can be constructed using Resistor-Transistor Logic (RTL) but are seldom used because of the propagation delay and power consumption.
- The NOR gate is termed a Universal Gate because of its capability to form any other logic using only NOR gates.
- The logic NOR gates commercially available have up to four NAND logic inputs. However, inputs can be extended by using cascaded NOR logic gates.
- The NOR logic circuit having an odd number of inputs can be constructed by using a pull-down resistor on the unused pin.
- An external circuit can be controlled by NOR logic with the use of a magnetic relay.