Unit 1

Digital Principle

Q1) Compare Analog and digital signals.

A1)

Q2) Calculate the Decimal Equivalent of binary number 101112

A2)

Q3) Calculate the Decimal Equivalent of Hexadecimal Number: 19FDA16

A3)

Q4) Explain XS-3 and Gray Code.

A4)

Excess-3 code

• It is also known as XS-3 code.
• It is a non-weighted code used to express decimal numbers.
• They are derived from the 8421 BCD code words adding (0011)2 or (3)10 to each code word in 8421.
• The excess-3 codes are obtained as  −

Example

                                         Fig.: BCD to XS 3 conversion (Ref. 1)

Gray Code

• It is the non-weighted code and is not an arithmetic code.
• This means that there are no specific weights assigned to the bit position.
• Here only one bit will change every time the decimal number is incremented .
• The gray code is also known as a unit distance code as only one bit changes at a time.
• The gray code is a type of cyclic code.
• It cannot be used for all arithmetic operation.

                                         Fig.: Gray codes  (Ref. 1)

Q5) Explain BCD code with advantages and disadvantages.

A5)

• Here each decimal digit is represented by a 4-bit binary number.
• Its a way to express each of the decimal digits with a binary code.
• Therefore, by four bits we can represent sixteen numbers (0000 to 1111).
• But in BCD code only first ten of these numbers are used (0000 to 1001) and rest are invalid.

                                             Fig.: BCD codes (Ref. 1)

Advantages of BCD Codes

• It is very similar to decimal system.
• We have to remember binary equivalent of 0 to 9 only.

Disadvantages of BCD Codes

• The addition and subtraction of BCD number system have different rules.
• The BCD arithmetic is more complicated.
• BCD code requires more number of bits than binary code to represent the decimal number.
• Hence is less efficient than binary.

Q6) Draw and explain basic gates.

A6)

The basic gates are namely AND gate, OR gate & NOT gate.

AND gate

It is a digital circuit that consists of two or more inputs and a single output which is the logical AND of all those inputs. It is represented with the symbol ‘.’.

The following is the truth table of 2-input AND gate.

Here A, B are the inputs and Y is the output of two input AND gate.

If both inputs are ‘1’, then only the output, Y is ‘1’. For remaining combinations of inputs, the output, Y is ‘0’.

The figure below shows the symbol of an AND gate, which is having two inputs A, B and one output, Y.

                                         Fig. : AND gate (ref. 1)

Timing Diagram:

OR gate

It is a digital circuit which has two or more inputs and a single output which is the logical OR of all those inputs. It is represented with the symbol ‘+’.

The truth table of 2-input OR gate is:

Here A, B are the inputs and Y is the output of two input OR gate.

When both inputs are ‘0’, then only the output, Y is ‘0’. For remaining combinations of inputs, the output, Y is ‘1’.

The figure below shows the symbol of an OR gate, which is having two inputs A, B and one output, Y.

                                                     Fig. : OR gate (ref. 1)

Timing Diagram:

NOT gate

It is a digital circuit that has one input and one output. Here the output is the logical inversion of input. Hence, it is also called as an inverter.

The truth table of NOT gate is:

Here A and Y are the corresponding input and output of NOT gate. When A is ‘0’, then, Y is ‘1’. Similarly, when, A is ‘1’, then, Y is ‘0’.

The figure below shows the symbol of NOT gate, which has one input, A and one output, Y.

                                             Fig. : NOT gate (ref. 1)

Timing Diagram:

Q7) Draw and explain universal gates.

A7)

• NAND & NOR gates are known as universal gates.
• We can implement any Boolean function by using NAND gates and NOR gates alone.

NAND gate

It is a digital circuit which has two or more inputs and single output and it is the inversion of logical AND gate.

The truth table of 2-input NAND gate is:

Here A, B are the inputs and Y is the output of two input NAND gate. When both inputs are ‘1’, then the output, Y is ‘0’. If at least one of the input is zero, then the output, Y is ‘1’. This is just the inverse of AND operation.

The image shows the symbol of NAND gate:

                                              Fig.: NAND gate (ref. 1)

NAND gate works same as AND gate followed by an inverter.

Timing Diagram:

NOR gate

It is a digital circuit that has two or more inputs and a single output which is the inversion of logical OR of all inputs.

The truth table of 2-input NOR gate is:

Here A and B are the two inputs and Y is the output. If both inputs are ‘0’, then the output is ‘1’. If any one of the input is ‘1’, then the output is ‘0’. This is exactly opposite to two input OR gate operation.

The symbol of NOR gate is:

                                                  
                                                           Fig.: NOR gate (ref. 1)

NOR gate works exactly same as that of OR gate followed by an inverter.

Timing Diagram:

Q8) Explain Ex-OR gate

A8)

It stands for Exclusive-OR gate. Its function varies when the inputs have even number of ones.

The truth table of 2-input Ex-OR gate is:

Here A, B are the inputs and Y is the output of two input Ex-OR gate. The output (Y) is zero instead of one when both the inputs are one.

Therefore, the output of Ex-OR gate is ‘1’, when only one of the two inputs is ‘1’. And it is zero, when both inputs are same.

The symbol of Ex-OR gate is as follows:

                                                           Fig.: XOR gate (ref. 1)

It is similar to that of OR gate with an exception for few combination(s) of inputs. Hence, the output is also known as an odd function.

Timing Diagram:

Q9) Explain Ex-NOR gate

A9)

It stands for Exclusive-NOR gate. Its function is same as that of NOR gate except when the inputs having even number of ones.

The truth table of 2-input Ex-NOR gate is:

Here A, B are the inputs and Y is the output. It is same as Ex-NOR gate with the only modification in the fourth row. The output is 1 instead of 0, when both the inputs are one.

Hence the output of Ex-NOR gate is ‘1’, when both inputs are same and 0, when both the inputs are different.

The symbol of Ex-NOR gate is:

                                       Fig.: XNOR gate (ref. 1)

It is similar to NOR gate except for few combination(s) of inputs. Here the output is ‘1’, when even number of 1 is present at the inputs. Hence is also called as an even function.

Timing Diagram: