Test: Combinational Logic - Electronics and Communication Engineering (ECE) MCQ

1st output of AND gate is = A’B’
2nd AND gate’s output is = AB and,
OR gate’s output is = (A’B’)+(AB) = AB + A’B’.

After solving the circuit we get (A’B’)+AB as output, which is XNOR operation. Thus, it will produce 1 when inputs are even number of 1s or all 0s, and produce 0 when input is odd number of 1s.

To determine which combination of logic gates can decode the binary data 1101, we need to understand the function of a decoder and how the specified logic gates operate

1. Understanding the Binary Data
   The binary data 1101 corresponds to the decimal number 13. A decoder is designed to activate a specific output line corresponding to the binary input. For a 4-bit binary input, there are 2⁴ = 16 possible combinations, and thus 16 output lines

2. Function of the 4-input AND Gate
   A 4-input AND gate outputs a high signal (1) only when all its inputs are high (1). To decode the binary number 1101, we can connect the inputs of the AND gate to the binary digits. The inputs would be:

   • Input 1 (A) = 1
   • Input 2 (B) = 1
   • Input 3 (C) = 0
   • Input 4 (D) = 1

3. Using an Inverter
   Since the third input (C) is 0, we need to invert this input to achieve a high output. An inverter will take the input C (which is 0) and output 1. Thus, we can connect the output of the inverter to the AND gate, allowing it to produce a high output when the other inputs are also high

4. Combining the Gates
   By using one 4-input AND gate and one inverter, we can effectively decode the binary input 1101. The AND gate will receive the inverted input for C, ensuring that the output is high when the binary code 1101 is presented

Thus, the correct combination of gates that can decode the binary data 1101 is one 4-input AND gate and one inverter

In the given diagram, S0 and S1 are selection bits. So,
I/P S0 S1 O/P
D = 0 0 0 Y0
D = 0 0 1 Y1
D = 0 1 0 Y2
D = 0 1 1 Y3
Hence, inputs are S0 and S1 are Low means 0, so output is Y0 and rest all are HIGH.

Full Adder is a combinational circuit with 3 input bits and 2 output bits CARRY and SUM. Three bits full adder requires 23 = 8 combinational circuits.

The given diagram is demultiplexer, because it takes single input & gives many outputs. A demultiplexer is a combinational circuit that takes a single output and latches it to multiple outputs depending on the select lines.

When both inputs are same then the o/p is high for a XNOR gate.
i.e., A B O/P
0 0 1
0 1 0
1 0 0
1 1 1.
Thus, it will produce 1 when inputs are even number of 1s or all 0s, and produce 0 when input is odd number of 1s.

Combinational Logic circuits are circuits for which the present output depends only on the present input, i.e. there is no memory element to store the past output.

A combinational circuit can have ‘n’ number of inputs and ‘m’ number of outputs as shown:

Code conversion circuits are used to convert a digital code from one format to another. For example, a binary code can be converted to a Gray code, or a BCD (binary-coded decimal) code can be converted to a binary code. These circuits typically use a combination of logic gates, such as AND gates, OR gates, and XOR gates, to perform the necessary conversions.

However, the most commonly used type of circuit for code conversion is the AND-OR gate circuit. This circuit is based on a combination of AND gates and OR gates, and it can be used to implement various types of code conversion, such as binary to Gray code conversion and BCD to binary conversion. The AND-OR gate circuit is preferred for code conversion because it is simple, efficient, and provides a high level of flexibility.

Designing a combinational circuit typically involves 4 steps:

1. Problem specification: This involves identifying the problem that the circuit needs to solve, and defining the input and output requirements.

2. Truth table creation: This involves creating a truth table that shows the desired output for each possible combination of input values.

3. Boolean expression derivation: This involves deriving a Boolean expression or set of expressions that represent the desired output in terms of the input variables.

4. Logic diagram implementation: This involves implementing the Boolean expressions using logic gates, such as AND, OR, NOT, XOR, etc.

These 4 steps provide a systematic approach to designing combinational circuits that can be used for a wide range of problems. However, the number of steps required may vary depending on the complexity of the problem and the circuit being designed.