AND gate

Implementations

In logic families like TTL, NMOS, PMOS and CMOS, an AND gate is built from a NAND gate followed by an inverter. In the CMOS implementation above, transistors T1-T4 realize the NAND gate and transistors T5 and T6 the inverter. The need for an inverter makes AND gates less efficient than NAND gates.

AND gates can also be made from discrete components and are readily available as integrated circuits in several different logic families.

Analytical representation

${\displaystyle f(a,b)=a\ast b}$ is the analytical representation of AND gate:

• ${\displaystyle f(0,0)=0\ast 0=0}$
• ${\displaystyle f(0,1)=0\ast 1=0}$
• ${\displaystyle f(1,0)=1\ast 0=0}$
• ${\displaystyle f(1,1)=1\ast 1=1}$

Alternatives

If no specific AND gates are available, one can be made from NAND or NOR gates, because NAND and NOR gates are "universal gates" meaning that they can be used to make all the others.

AND gates with multiple inputs

AND gates with multiple inputs are designated with the same symbol, with more lines leading in. While direct implementations with more than four inputs are possible in logic families like CMOS, these are inefficient. More efficient implementations use a cascade of NAND and NOR gates, as shown in the picture on the right below. This is more efficient than the cascade of AND gates shown on the left.