How Do NAND Gates Work?

Truth tables are helpful for working out exactly how your NAND gate will perform in a circuit. Working under the Boolean function, they help you to figure out what the output will be as a result of multiple inputs. 

In these tables, binary inputs and outputs are used. This means when the input is true (a signal is high or a switch is turned on) this is noted as a 1 and when the input is false (a signal is low or a switch is turned off) a 0 is used. 

For NAND gates, the logic is that the output is 1 (or true) when all of the inputs are 0 (or false). In all other cases, the output is 0 (or false).

As such, the truth table logic for a NAND gate works like this:

As circuits get more complex and extra inputs are added, these truth tables can grow accordingly. For example, a four-input NAND gate truth table will be expressed like this:

When building a circuit using NAND gates, having a truth table with the correct number of inputs can help you work out exactly how the signal flow will work, ensuring you put the gates in the right place to reach the desired output.

Using only NAND gates won’t just help to control and invert multiple inputs but can be used for a variety of logical functions. Specifically, a NAND gate will make the output true when all the inputs are false and vice versa. This means the output won’t change when the signal drops or a switch is turned off in one of the inputs. 

This effect is also known as a Sheffer stroke and can be used in a variety of ways, including:

• In home security systems: if sensors are attached to all windows and doors, they can send a signal 1 to the circuit when these are closed. This makes the alarm output 0. Then, if a sensor detects that a window or door is open, its signal will change to a 0. The alarm output will then become 1, setting off a sound or another function
• In freezer warning buzzers: in this case, the NAND gate is used as a NOT gate due to a single input. This means as the temperature gets warmer, the signal of the inputs drops towards 0. This causes the output to switch to 1, triggering an alarm or other warning system
• In light-activated burglar alarms: the two inputs in these systems are a switch and a light-dependent resistor (LDR). When the switch is closed or the LDR is in the light, these inputs will be 0, meaning the output will change to 1 and an alarm system will be triggered

NAND gates might also be chosen for a circuit due to their cost-effectiveness, durability, large storage capacity relative to their size, and the ease of replacing them if their flash memory is damaged. 

The exact method of converting to NAND gates circuits will depend on the specific circuit’s function, complexity, and the types of gates currently being used.

However, there are a few rules which are helpful to keep in mind when making the conversion:

NAND and NOR gates are called universal gates because they work under the Boolean function logic. Also known as logical gates, they follow binary functions and are part of a larger group of gates, including NOT, AND, OR, XOR and XNOR. As part of this group, both NAND and NOR gates can be used to recreate the function of the others in a circuit. 

Similarly to a NAND gate, an OR gate converts two inputs into one output. An OR gate makes the output true (equivalent to 1) when either input is also true (equivalent to 1) and not when they are both true or false (equivalent to 0). 

Therefore, to recreate an OR gate, three NAND gates need to be used (if the first two inputs can’t be combined). The main two inputs will be split and put into separate NAND gates. To recreate the OR function, these inputs then need to both be fed into a final NAND gate, reversing the initial inversion and producing an equivalent output.