4 bit magnitude comparator

1. INTRODUCTION TO 4 BIT
COMPARATORS
UNDERSTANDING DIGITAL LOGIC

2. AGENDA
• Definition of comparator
• Basic logic gates
• Circuit diagram
• Flowchart
• Input & output
• Truth table
• Logic gates
• Operation
• Applications
• Limitations
• Advantages and disadvantages
• Advanced technology (4 bit comparator)
• Reference

3. DEFINITION OF COMPARATOR
Comparatorshave analog input terminals and one binary
digital output. They are used to compare a measurable
quantity with a reference or standard
ROLE IN DIGITAL ELECTRONICS:
Digital comparatoris a hardware device that compares
two binary numbers and determines whether one number is
greater than, less than, or equal to the other and
comparators are used in central processing units (CPUs)
,Microcontrollers(MCUs)

4. BASIC LOGIC GATES
AND GATES
• An AND gate is a logic gate that has two or more inputs
and a single output. It operateson logical multiplication
rules. The output is high (1) only if all of the inputs are
high (1). If either of the inputs is low (0), then the output
is also low.
OR GATES
• An OR gate is a digital logic gate that performs logical
disjunction. It produces a high output (1) when any of its
inputs are high. The gate’s output is low (0) only when all
its inputs are low
NOT GATE
• A NOT gate is a logic gate that inverts the input signal.
It’s also known as an inverter. A NOT gate has one input
and one output. It produces a high output when given a
low input, and a low output when given a high input. The
Boolean logic for a NOT gate is Z= ~A for an input

5. CIRCUIT DIAGRAM

6. FLOWCHART

7. INPUT AND OUTPUT
• The 4-bit input lines A and B are like
switches that can be either on or off.
They help us input binary numbers.
• To determine the outputs A > B, A < B,
and A = B, we compare the values of
the input lines A and B. If A is greater
than B, the output A > B is true. If A is
less than B, the output A < B is true. And
if A is equal to B, the output A = B is
true. It's like comparing numbers to see
which one is bigger, smaller, or equal.

8. Sure! Here's a truth table for a 4-bit comparator:
| A > B | A < B | A = B |
|-------|-------|-------|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 0 | 0 | 1 |
In this table, the outputs A > B, A < B, and A = B change based
on the combinations of values for the 4-bit input lines A and B.
For each row in the table, the outputs are determined by
comparing the corresponding bits of A and B. If the bit in A is
greater than the corresponding bit in B, then A > B is 1 and the
other outputs are 0. If the bit in A is less than the corresponding
bit in B, then A < B is 1 and the other outputs are 0. If the bits in
A and B are equal, then A = B is 1 and the other outputs are 0.
TRUTH TABLE

9. In a comparator, logic gates like AND, OR, and XOR are used to
perform the comparison. Let me break it down for you:
1. AND gate: It checks if both input bits are 1. If both bits are
1, the output of the AND gate is 1; otherwise, it's 0.
2. OR gate: It checks if at least one input bit is 1. If either or
both bits are 1, the output of the OR gate is 1; otherwise, it's
0.
3. XOR gate: It checks if the input bits are different. If the bits
are different, the output of the XOR gate is 1; otherwise, it's
0.
4. By combining these gates in a specific configuration, the
comparator circuit compares the corresponding bits of A and
B and generates the outputs A > B, A < B, and A = B based
on the results of these logic gate operations. This allows us to
determine the relationship between the binary values of A
and B.
LOGIC GATES

10. Let me explain step-by-step how the comparator compares A and B using a flowchart:
1. Start by taking the binary values of A and B as inputs.
2. Compare the most significant bits (MSBs) of A and B using an XOR gate. If they are different, go
to step
3. Otherwise, go to step 4.3. If the MSBs are different, check if the MSB of A is 1. If it is, output A >
B. Otherwise, output A < B.
4. If the MSBs are the same, move on to the next bit and repeat steps 2-4 for the remaining bits.
5. Continue this process until all bits have been compared.
6. Once all bits have been compared, if all the bits are the same, output A = B.
OPERATION

12. 4-bit comparatorshave variousreal-world applicationsin digital systems and
electronics. They are used to compare two 4-bit binary numbers,typically A
and B, and produce outputs indicating the result of the comparison.Here are
some common applications:
1.Magnitude Comparison:4-bit comparatorsare used to
determine whether one 4-bit binary number is greater than,
less than, or equal to another.
2.Data Sorting: In microcontrollersand microprocessors, 4-bit
comparatorsare used to sort data.
3.Multiplexers and Demultiplexers:Comparatorscan be used
in multiplexersto select a specific input based on comparison
results.
4.Control Logic: In digitalcontrol systems, comparators are
utilized to create decision-makinglogic.
5.Alarm Systems: In security and alarm systems, 4-bit
comparatorscan be used to compare sensor inputs
APPLICATIONS

13. 4-bit comparatorsare essential components in digital systems, but
they come with some limitationsand potentialissues, particularlyin
terms of accuracy and speed:
1. Limited Resolution:The most obviouslimitationis the
limited resolutionof 4 bits. They can only represent 16 discrete
values (2^4), which may not be sufficient for applicationsthat
require fine-grained comparisons.
2. Accuracy: The accuracy of 4-bit comparatorsis restricted by
the limited number of bits. Small variationsin input values can
lead to incorrect comparisons.
3. Speed: 4-bit comparatorscan perform fast comparisons, but
their speed can be a limitation whenextremely high-speed
comparisonsare necessary, as is the case in some advanced
digitalsignal processing applicationsor high-frequency
communicationsystems. In such cases, faster comparatorswith
more bits are required. Etc
LIMITATIONS

14. 4-Bit Comparators: Advantages:
1.Simplicity: 4-bit comparatorsare relativelysimple in terms of
design and implementation,making them cost-effective and
suitablefor less complex applications.
2.Lower PowerConsumption:Compared to larger bit
comparators,4-bit versions tend to consume less power, which
can be advantageousin battery-operated devices.
Disadvantages:
1.Limited Precision:The main drawbackof 4-bit comparatorsis
their limited precision. They can only represent 16 discrete
values, which may not be sufficient for applicationsthat
demand high accuracy.
2.Accuracy: Due to their limited bit width, 4-bit comparators
are less accurate when comparing values with small
differences.
ADVANTAGES & DISADVANTAGES

15. ADVANCED TECHNOLOGY (4- BIT COMPARATOR)
To implement an advanced technology 4-bit magnitude
comparator, you would typically use digital logic gates, such
as AND, OR, and XOR gates, along with flip-flops and
possibly multiplexers or programmable logic devices.
Advanced technology of 4 bit comparator uses cascading
method.
significantCascading: For a 4-bit magnitude comparator, you
can cascade four 1-bit comparators to handle the comparison
of all four bits.
Advanced technology might involve the use of smaller and
faster logic gates, more compact designs, and lower power
consumption. You can implement this comparator using
hardware description languages like VHDL or Verilog, and
then synthesize the design to fit a specific integrated circuit
technology.

16. REFERENCE
https://youtu.be/WSJwKRBWax0?si=TcAGJSK5i9XwWSj_https://youtu.be/
WSJwKRBWax0?si=TcAGJSK5i9XwWSj_

17. GOPI KRISHNAN M ( RA2211004010355)
AADHI P (RA2211004010352)
PRABAKARAN T (RA2211004010345)