NAND is an abbreviation for “NOT AND.”
A two-input NAND gate is a digital combination logic circuit that performs the logical inverse of an AND gate. While an AND gate outputs a logical “1” only if both inputs are logical “1,” a NAND gate outputs a logical “0” for this same combination of inputs. The symbol and truth table for a NAND gate is shown in Figure 1. The Boolean expression for a NAND gate with two inputs (A, B) and output X is:
Figure 1. Symbol and truth table for NAND gate
NAND gates help detect if a single input to a digital system has gone low. For example, a simple security system consisting only of NAND gates could be used to monitor the status of sensors connected to windows and/or doors. If a window/door is closed, the sensor sends a logical “1” signal to the security system. While all windows and doors are closed, the alarm output is “0.” If a single window or door is opened, the security system output changes state to become “1” and this can be used to trigger an alarm or take some other action.
The popularity of the NAND gate is derived from the fact that it is the easiest of the digital logical operators to implement using transistor technology, e.g., a two-input NAND gate uses only four transistors when implemented in CMOS. All other logical operators can be implemented using only NAND gates connected in different configurations. Early microprocessors were implemented using only this trivial circuit.