BE Lab Manual Experiment 3

Experiment 3

Aim:-To study the NAND & NOR gate as universal gates.

Apparatus: - NAND & NOR gate as universal gate kit, patch chords. 

Theory: - The basic building block of any digital circuit is a logic gate. These logic gates operate with binary numbers. This logic gate can be constructed by using ICs. The logic gates have one or more inputs and only one output. The most basic gates are AND, OR, & NOR. Other gates are NOR & NAND. Other than these gates two more gates are known that are EX-OR & EX – NOR. The NAND & NOR gates are called universal gates because only using these gates we construct any gate. 

NAND GATE AS UNIVERSAL GATE 

NAND gate as a universal gate:

Since all types of gates can be constructed with the help of the NAND gate, it is referred to as a universal gate. A NAND gate has two or more inputs labeled A, B, C but has only one output Y. in a NAND gate the output is low (logic 0) if all the inputs are high (logic 1). For other combinations of inputs the output is high (logic 1). The symbol and the truth table of the NAND gate are shown in figure (1).

Truth table

Circuit

The IC 7400 is a NAND gate IC. The pin configuration of IC7400 is shown in the figure.

  1. NAND gate as a AND gate
The AND gate has two inputs A & B and only one output Y. the output of  AND gate is high logic (logic 1) if both the inputs are high otherwise output is low (logic 0). The AND gate can be contracted by using two NAND gates as shown in figure (2).

The truth table for AND gate

Circuit

Procedure 1:

  • Study the logic diagram of AND gate using the NAND gate (shown in figure 2).
  •  Apply the logic input (1 or 0), using patch chords to the input A & B    and observe the output Y.
  • Verify the truth table of AND gate (table 1) for different input levels.

2.      NAND gate as an OR gate

The OR gate has two inputs A & B and one output Y. when both the inputs are at logic 0 then only the output becomes low (logic 0) otherwise the output is the logic diagram (2).

Circuit:-

The truth table for the OR gate is given below.


Procedure 2:
  • Study the logic diagram of the OR gate using NAND gate (shown in figure3).
  • Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output Y by connecting the output terminal to logic output indicator terminals. 
  • Verify the truth table of the OR gate (table 2) for different input levels.

3. NAND gate as a NOR/NAND gate

Using a NAND gate, a not gate can also be constructed. The constructed diagram for NOT gate using NAND gate is shown in figure (4).

Since the NOT gate has only one input, the two inputs of the NAND gate are shorted and named as input A. the output of the NOT gate is. The truth table is shown in table (3).
For NAND gate operation, connect two inputs A & B to the logic generator (1 or 0) and the output is AB. The truth table is given in table (4).
Procedure 3:-
  • For NOT gate short the input A & B using patch chord.
  • Apply the logic input (1 or 0), at A and observe the output Y.
  • Verify the truth table of NOT gate (table 3) for input levels.
  • For the NAND gate apply logic inputs (1 or 0) using patch chords to the input A & B and observe the output Y.
  • Observer the output Y by connecting the output terminal to the logic output indicators terminal.
  • Verify the truth table (table 4) by applying different input levels.

4. NAND gate as a NOR gate

A NOR gate has two inputs A & B and only one output Y, the output NOR gate is high if both the inputs A & B are at logic level 0. For other input conditions, the output is low (logic 0). A NOR gate can be constructed using four NAND gates. As shown in figure (5).

The truth table for the NOR gate is given in table (5).


Procedure 4:

  • Study the logic diagram of the NOR gate using the NAND gate (shown in figure 5).
  • Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output Y by connecting output terminal to logic output indicators terminal. 
  • Verify the truth table of OR gate (table 5) for different input levels.

5. NAND gate as an XOR gate:

The exclusive OR (XOR) gate has two input and one output. The output is low when its both the inputs are same (either logic 0 or logic 1) and is high output when it has two different input. (Input A high and input B low and vice versa). The construction diagram for the XOR gate is shown in figure (6).

The truth table for X - OR gate is given in table (6).
Procedure 5:-
  • Study the logic diagram of the XOR gate using NAND gate (shown in figure 6).
  • Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output Y. 
  • Verify the truth table of the XOR gate (table 6) for different input levels.

6. NAND gate as an X-NOR gate:

The exclusive NOR (X-NOR) gate has two input and one output. The output is high when both the inputs have same level (either logic 0 or logic 1) and the output is low when two inputs are of different types. (Input A low and input B high and vice versa). The construction diagram for the X-NOR gate is shown in figure (7).

The truth table for X - OR gate is given in table (7).
Procedure 6:
  • Study the logic diagram of the X-NOR gate using NAND gate (shown in figure7).
  • Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output Y.
  • Verify the truth table of X - NOR gate (table 7) for different input levels.

Result:

As the different gates AND, OR, NOT, NAND, NOR, XOR & X–NOR gates can be constructed using NAND gate, Hence NAND gate is known as universal gate.

NOR GATE AS UNIVERSIAL GATE

Theory:

The basic building block of any digital circuit is a logic gate. These logic gates operate with binary numbers. This logic gate can be constructed by using ICs. The logic gates have one or more inputs and only one output. The most basic gates are AND, OR, & NOT. Other gates are NOR & NAND. Other than these gates two more gates are known that are EX – OR & EX – NOR. The NOR & NAND gates are called as universal gates, because only using these gate we can construct gate.

NOR gate as universal gate

Since all the types of gats can be constructed only with the help of the NOR gate, it is referred as universal gate. A NOR gate has two or more inputs labeled A, B, C but has only one output Y. in NOR gate the output is low (logic 0) if all the inputs are high (logic 1) .For other combination of inputs the output is high (logic 1). The symbol and the truth table of NOR gate is shown in figure (1).

Truth Table

Circuit 

The IC 7402 is a NOR gate IC. The Pin configuration of IC 7402 is shown in figure 2.

1. NOR gate as a OR gate:

The OR gate has two input A & B and one output Y. When both the input are at logic 0 then only the output becomes low otherwise the output is high (logic 1). The OR gate can be constructed using two NOR gate as shown in the logic diagram 2.

The truth table for OR gate is given below.

Procedure 1:

  • Study the logic diagram of OR gate using NOR gate (shown in figure 2).
  • Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output Y. (1 for Red LED and 0 for Green LED).
  • Verify the truth table of OR gate (table 1) for different input levels.

2. NOR gate as a AND gate: 

The AND gate has two input A & B and only one output Y. the output of AND gate is high (logic 1) if both the inputs are high otherwise output is low (logic 0). The AND gate can be constructed by using three NOR gates as shown in figure 3.

The truth table for AND gate is given below.

Procedure 2:

  • Study the logic diagram of AND gate using NOR gate (shown in figure 3).
  • Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output Y by connecting output terminal to logic output indicators terminal. (1 for Red LED and 0 for Green LED).
  • Verify the truth table of OR gate (table 1) for different input levels.

3. NOR gate as a NOT / NOR gate:

Using NOR gate, a NOT gate can also be constructed. The construction diagram for NOT gate using NOR gate is shown in figure 4.

Since the NOT gate has only one input, the two inputs of NOR gate are shorted and named as input A. the output of NOT gate is given in table 3.

For NOR gate operation, connect two inputs A & B the output is  the truth table is given in table 4.

Procedure 3:-

  • For NOT gate short the input A & B using patch chord.
  • Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output Y. (1 for Red LED and 0 for Green LED).
  • Verify the truth table of the OR gate (table 3) for different input levels.
  • For NOR gate apply two input A & B from logic 1 and logic 0.
  • Observe the output Y at output 1 / 0. (1 for Red LED and 0 for Green LED).
  • Verify the truth table of OR gate (table 4) for different input levels.

4. NOR gate as a NAND gate:-

A NAND has two inputs A & B and only one output Y. The output of NAND gate is low if both the inputs A & B are at logic level 1. For other cases the output is high (logic 1). To construct a NAND gate using NOR gate it requires four nor gates. The constructional diagram for NAND gate   is shown in figure 5. The truth table for NAND gate is given in table5. 

 

Procedure 4:

  • Study the logic diagram of the NAND gate using NOR gate (shown in figure 5).
  • Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output by connecting output terminal to logic output indicators terminal (1 for Red LED and 0 for Green LED).
  • Verify the truth table of NAND gate (table 5) for different input levels.

5. NOR gate as an XOR gate:

The Exclusive OR (X-OR) gate has two inputs and one output. The output is low when both the inputs are same (either logic 0 or logic 1) and high output when it has two different input. (input A high and input low and vice versa). The construction diagram for the XOR gate is shown in figure 6.

The truth table for X–OR gate is given in table 6.

Procedure 5:

  • Study the logic diagram of the X-OR gate using NOR gate (shown in figure 6).
  • Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output Y. (1 for Red LED and 0 for Green LED).
  • Verify the truth table of the X-OR gate (table 6) for different input levels.

6. NOR gate as an X–NOR gate:

The Exclusive NOR (X - NOR) gate has two inputs and one output. The output is high when both the inputs have same level (either logic 0 or logic 1) and the output is low when two inputs are of different. (Input A low and input B low and vice versa). The construction diagram for X – NOR gate is shown in figure 7.

Circuit:- 

The Truth table for the X–NOR gate is given in table 7 below.

Procedure 6:

  • Study the logic diagram of the X-NOR gate using NOR gate (shown in figure 7).
  •  Apply the logic input (1 or 0), using patch chords to the input A & B and observe the output Y. (1 for Red LED and 0 for Green LED).
  • Verify the truth table of X - NOR gate (table 7) for different input levels.

Result: - NOR as an universal gate is studied.

Comments

Post a Comment

Popular posts from this blog

BCA Syllabus Topics

SEMESTER-2 nd Course: BCA SUBJECT: DIGITAL COMPUTER ORGANIZATION Syllabus : Unit-I : Digital computer and digital system; Binary number system: number base conversion. Compliments: one's, two's, 9's and 10's complements code: Gray BCD, ASCII, and error detection code. Logic Gates: AND, OR, NOT, EX-OR, Universal gate. Logic Circuit. Boolean function: Rules and simplification, simplification of Boolean function using map method, don't care condition. Unit-II: Combinational Circuits: Adders, Subtractors, Multiplexer, Demultiplexer Decoder, Encoder) Sequential Circuit: Flip-Flop: RS, Clocked RS, JK, D flip-flop, and Master board, Case studies to understand organization of laptop like Dell, Lenovo etc. slave flip-flop. Register- Introduction, Shift register, serial Transfer & parlor Load. Counters- Ripple Counter (Asynchronous), Synchronous Counters. Unit-III: 8086 internal architecture, register organization of 8086, addressing modes, instruction set and assembler ...
Read more

Quine-Mccluskey Method

Image
 Quine-Mccluskey Method It also known as Tabular method. It is more systematic method of minimizing expressions of even larger number of variables. It is suitable for hand computation as well as computation by machines i.e., programmable. . The procedure is based on repeated application of the combining theorem.  PA+P =P (P is set of literals) on all adjacent pairs of terms, yields the set of all PI‘s from which a minimal sum may be selected.  Consider expression ∑m(0,1,4,5)= + C+A +A C First,  second terms & third, fourth terms can be combined ( + ) + (C+ )= + A Reduced to (      +    ) = The same result can be obtained by combining m 0 & m 4 & m 1 &m 5 in first step & resulting terms in the second step. Procedure: Decimal Representation Don‘t cares PI chart EPI Dominating Rows & Columns Determination of Minimal expressions in c...
Read more

Alternate Logic-Gate Representations

Image
Alternate Logic-Gate Representations We have discussed the five basic logic gates (AND, OR, INVERTER, NAND, and NOR) and the standard symbols used to represent them in a logic circuit diagram. Most of the logic networks use standard symbols. But in some networks an alternative set of symbols is used in addition to the standard symbols. The table shows the alternate set of symbols for the five basic gates. Table: Alternate Logic Gate Representations To convert any normal symbol to its corresponding alternate symbol, the following steps are used: METHODOLOGY: TO CONVERT STANDARD SYMBOL TO ALTERNATE SYMBOL Step 1: Add bubbles (indication of inversion) at those input or output points where it is not present. Step 2: Remove all pre-existing bubbles of the normal symbol, if there is any at the point (only NOT, NAND and NOR gates) Step 3: If the existing normal logic symbol is AND, change it to OR, Similarly, if it is OR, then change it to AND. There is no change for the triangular symbol of ...
Read more