The output state of a digital logic AND gate only returns “LOW” again when ANY of its inputs are at a logic level “0”. In other words for a logic AND gate, any LOW input will give a LOW output.
The logic or Boolean expression given for a digital logic AND gate is that for Logical Multiplication which is denoted by a single dot or full stop symbol, ( . ) giving us the Boolean expression of: A.B = Q.
Then we can define the operation of a digital 2-input logic AND gate as being:
“If both A and B are true, then Q is true”
2-input Transistor AND Gate
A simple 2-input logic AND gate can be constructed using RTL Resistor-transistor switches connected together as shown below with the inputs connected directly to the transistor bases. Both transistors must be saturated “ON” for an output at Q.
Logic AND Gates are available using digital circuits to produce the desired logical function and is given a symbol whose shape represents the logical operation of the AND gate.
Digital Logic “AND” Gate Types
The 2-input Logic AND Gate
| Symbol | Truth Table | ||
2-input AND Gate
|
B | A | Q |
| 0 | 0 | 0 | |
| 0 | 1 | 0 | |
| 1 | 0 | 0 | |
| 1 | 1 | 1 | |
| Boolean Expression Q = A.B | Read as A AND B gives Q | ||
The 3-input Logic AND Gate
| Symbol | Truth Table | |||
3-input AND Gate
|
C | B | A | Q |
| 0 | 0 | 0 | 0 | |
| 0 | 0 | 1 | 0 | |
| 0 | 1 | 0 | 0 | |
| 0 | 1 | 1 | 0 | |
| 1 | 0 | 0 | 0 | |
| 1 | 0 | 1 | 0 | |
| 1 | 1 | 0 | 0 | |
| 1 | 1 | 1 | 1 | |
| Boolean Expression Q = A.B.C | Read as A AND B AND C gives Q | |||
Because the Boolean expression for the logic AND function is defined as (.), which is a binary operation, AND gates can be cascaded together to form any number of individual inputs. However, commercial available AND gate IC’s are only available in standard 2, 3, or 4-input packages. If additional inputs are required, then standard AND gates will need to be cascaded together to obtain the required input value, for example.
Multi-input AND Gate
The Boolean Expression for this 6-input AND gate will therefore be:
Q = (A.B).(C.D).(E.F)
In other words:
A AND B AND C AND D AND E AND F gives Q
If the number of inputs required is an odd number of inputs any “unused” inputs can be held HIGH by connecting them directly to the power supply using suitable “Pull-up” resistors.
Commonly available digital logic AND gate IC’s include:
TTL Logic AND Gate
- 74LS08 Quad 2-input
- 74LS11 Triple 3-input
- 74LS21 Dual 4-input
CMOS Logic AND Gate
- CD4081 Quad 2-input
- CD4073 Triple 3-input
- CD4082 Dual 4-input
7408 Quad 2-input AND Gate
In the next tutorial about Digital Logic Gates, we will look at the digital logic OR Gate function as used in both TTL and CMOS logic circuits as well as its Boolean Algebra definition and truth tables.
