**Digital Logic AND Gate**

Table of Contents

**What is a Logic Gate?**

A **logic gate** is used to implement **Boolean function** by performing a logical operation. It ta kes **binary logic** as **input** and produces** binary logic** as an **output**.

A logic gate is basically the building block of a digital circuit. All the digital systems within the world are composed of logic gates.

Logic gates work on **binary Logic** refer as **High-State “1”** and **Low-State “0”**.

These gates have usually two inputs and one output. Combinations of **Binary Logic Low ”0”** and** logic High ”1”** is given as inputs to these logic gates, and their corresponding output is produced based on their **Boolean** functions.

**Good to know:**

*These terms also used in binary logic gates and circuits*

**0** or **1**

**Low** or **High**

**True** or **False**

**ON** or **OFF**

**Basic And Derived Logic Gates**

**AND, OR, NOT, NAND, NOR** are the basic logic gates. Basic gate combines together to form Derived logic gates like** XOR, XNOR** etc.

**What is Logic AND Gate**

**AND Gate** is a basic logic gate which provides **High-State “1” **once all of the inputs to the **AND Gate** are **High-State”1”**. If any of the input is **Low-State ”0”,** than its output is **Low-State ”0” **.It is also referred to as arithmetic multiply operation.

**AND Gate Logic Symbol, Boolean Expression & Truth Table**

**AND Gate Symbol**

There are 3 types of symbols used for **AND gate** all over the world

**American National Standards Institute** (**ANSI)/ MILITARY**

**International Electrotechnical Commission** (**IEC)/EUROPEAN**

*Deutsches Institut für Normung (DIN)/GERMANY*

**Boolean Expression **

*C = A.B **or **C = A & B*

**Truth Table**

A mathematical table used to specify input to output logic combination of a digital circuit is known as a **truth table**, the truth table of **AND Gate **is given below.

**AND Gate Logic Flow Schematic Diagram**

**Construction and Working Mechanism of AND Gate:**

**AND Gate using Resistor-Diode Logic(RDL)**

In ** Resistor-Diode Logic (RDL),** the diode is used as a switch. In

**AND Gate**diodes are placed in such configuration when

*,***any of the two input**is

**logic-Low “0”,**the corresponding diode will become

**forward bias**and

**logic-Low”0**” will flow through output as there is no resistance in its path. When both inputs are

**logic-High”1”**diodes will be reversed biased, Hence

**Vsupply**(

**Logic High state**) will be routed to

**output C**as

**“1”.**

**NOTE: **There is always diode **forward voltage drop** of approximately **0.7 volts** in the case of **silicon** and **0.3 volts** in the case of the **germanium diode**.

**AND Gate using Resistor-Transistor Logic*** (RTL)*

*(RTL)*

In ** Resistor-Transistor Logic (RTL),** the main switching unit is the transistor. In the figure given below, there are 2

**NPN transistors**connected in series that switches on with

**logic level high ”1”**, when both of the transistors are turned on,

**Vcc”1”**will flow through

**output**. There is a pull-down resistor connected to the output, Therefore there will be always

**Logic-Low”0”**at the output unless both of the transistors are switched on.

**NOTE**: **RTL **logic **limitation** or **disadvantage** is that it has **high power dissipation** due to current flow in base resistors and collector resistors when the **BJT’s** are switched on.

**AND Gate using MOS Logic**

In ** MOS Logic**,

**MOSFETs**are used as the main switching unit. As you can see in the figure below the two

**MOSFET**in series are being controlled by the inputsignal, In turn, these

**NMOSFETs**control the other

**NMOSFET**. When both inputs are

**High-State”1”**, the

**NMOS**connected in series activates and successively,

**NMOS**on the OUTPUT side is

**switched off**due to

**logic low gate input (GND)**. Thus the only route to output is from Vdd (Logic high).

When any of this input is **Low-State”0”**, the **NMOS connected in series** will be **switched-off **resulting in **High State”1”** at the gate of **NMOS** on the OUTPUT side(Switched-on). As the NMOS is switched-on, therefore the **output C** will be directly connected to **GND (Low State”0”)**.

**AND Gate From Other Logic Gates**

**AND gate’s** function can be achieved by different combinations of different logic gate some of them are given below.

**BOOLEAN EXPRESSION:**

**AND Gate From NAND Gate**

**C = ((A.B)’)’**

**AND Gate From NOT-NOR Gate**

**C = A.B**

**C = (A’+B’)’**

**AND Gate From NOR GATE**

**C = (a’+b’)’**

**Multiple Input AND Gate**

As we have established before that **AND Gate** gives logic **High State”1” **only and only when all of its inputs are logic **High State”1”**. It’s**“n” number of inputs** truth table is given below:

**Truth Table**

**NOTE:** In the table given below **“X”** means **“don’t care”**. It can be **“1”**and it can be **“0”**. Which means, as long as there is a single input carrying **“0”**, the output will be always **“0”** so there is no reason to put a check on other inputs, that’s why it’s called **“don’t care X”.**

**What would you do if there are more than two inputs needed**? The answer is simple.

**Resistor-Diode Logic**

IN **RDL (Resistor-Diode logic)** logic, a diode is used on every input line, thus **adding diodes **can **increase the number of input lines** as shown in the **figure** below. Each input is fed to separate diode. Place as many diodes as you would like,to create a **Multi-Input AND GATE**.

**Resistor-Transistor Logic**

In **RTL (Resistor-Transistor Logic)**, Transistors are used as switching unit. To increase the input lines we have to **increase the number of transistors** connected in series as shown in the figure below.

**MOS Logic**

In **MOS logic**, the case is same as RTL logic, instead, we **increase the number of MOSFETs** connected in series at the input side. **AND GATE** with three input in MOS logic is given below. If you want to add another input, add another NMOS in series.

**Cascaded Setup of AND Gates**

**Multi-input AND gate** function can be achieved by cascading **Two-Input AND Gate** in a specific configuration given below

**OUT = IN _{1 }& IN_{2 }& IN_{3}**

**OUT = (IN _{1 }& IN_{2}) & IN**

_{3}

**OUT = IN _{1 }& IN_{2 }& IN_{3 }& IN_{4}**

**OUT = (IN _{1 }& IN_{2}) & (IN_{3 }& IN_{4})**

**TTL and CMOS Logic AND Gate IC’s**

Commercially up to **Four-Input AND gate** IC’s are available in the market, having two **AND gates** in a single package. Some of the ICs with Pin Details are given below.

**TTL Logic AND Gates**

- 74LS08 Quad 2-input
- 74LS11 Triple 3-input
- 74LS21 Dual 4-input

**CMOS Logic AND Gates**

- CD4081 Quad 2-input
- CD4073 Triple 3-input
- CD4082 Dual 4-input

**7408 TTL and 4081 CMOS AND Gate IC (Two-Inputs)**

**Pinout for 7408 TTL AND Gate IC**

PIN Number |
Description |

1 | Input Gate 1 |

2 | Input Gate 1 |

3 | Output Gate 1 |

4 | Input Gate 2 |

5 | Input Gate 2 |

6 | Output Gate 2 |

7 | Ground |

8 | Output Gate 3 |

9 | Input Gate 3 |

10 | Input Gate 3 |

11 | Output Gate 4 |

12 | Input Gate 4 |

13 | Input Gate 4 |

14 | Positive Supply Voltage |

**4073 CMOS and 7411 TTL AND Gate IC (Three-Inputs)**

**4082 CMOS and 7821 TTL AND Gate IC (Four-Inputs)**

**AND Gate Applications**

Common uses and application of AND gate are follow:

- As enable gate (Allowance of data through a channel).
- As inhibit gate (Reverse of enable gate i.e. disallowance of data through a channel).
- In the clock counters as enable and disable gate.
- Used in security devices e.g security lights and flood lights as PIR (Passive infrared) Device.
- In most of counting, computers and logic based digital circuits,

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