DESIGN AND EVALUATION OF A 4-BIT

BINARY SUBTRACTOR
▪ This document explores the design and implementation of a 4-bit binary subtractor
using full adders and logic gates. We will delve into the fundamental principles of
binary subtraction and full adder circuits, followed by a detailed explanation of the
subtractor circuit design. We will also assess the performance of this subtractor in
terms of gate count, delay, and power consumption. Finally, a comparison will be
drawn between this subtractor and a dedicated subtractor circuit, highlighting the
trade-offs involved.
INTRODUCTION TO BINARY SUBTRACTION
AND MOTIVATION FOR THE DESIGN
▪ Binary subtraction is a fundamental operation in digital electronics, used for
performing arithmetic calculations within computer systems. The subtraction operation
is performed by subtracting two binary numbers, producing a difference result. It forms
the basis for various arithmetic operations, such as addition, multiplication, and
division. Understanding binary subtraction is essential for designing digital circuits
capable of performing arithmetic operations.
▪
▪ The design and analysis of a 4-bit binary subtractor provide valuable insights into the
implementation of arithmetic operations using logic gates. By understanding the
underlying principles and techniques involved, we can develop a deeper appreciation
for the efficiency and complexity of digital circuits.
▪
▪ Furthermore, the comparison of our designed subtractor with a dedicated subtractor
circuit unveils the trade-offs associated with different design approaches. This allows us
to evaluate the strengths and limitations of each approach, paving the way for informed
decisions regarding circuit design and optimization.
PRINCIPLES OF FULL ADDER CIRCUITS
AND THEIR APPLICATION IN SUBTRACTION
▪ Full adder circuit is a fundamental building block in digital electronics, used to add two
binary digits along with a carry-in bit. It produces a sum bit and a carry-out bit. The full
adder circuit is crucial for implementing binary subtraction, as it allows for the
manipulation of binary numbers using addition.
▪
▪ In binary subtraction, we can utilize the concept of two’s complement to convert the
subtrahend into its negative equivalent. This allows us to perform subtraction using
addition, leveraging the functionality of full adders. The two’s complement of a binary
number is obtained by inverting all the bits of the original number and adding 1. By
adding the minuend and the two’s complement of the subtrahend, we effectively
perform binary subtraction.
▪
▪ For example, consider subtracting 0101 from 1100. The two's complement of 0101 is
1011. Adding 1100 and 1011 yields 10111. Ignoring the overflow bit, we get the
difference as 0111, which is the correct result of subtracting 0101 from 1100.
CIRCUIT DESIGN OF THE 4-BIT BINARY
SUBTRACTOR
▪ The 4-bit binary subtractor is designed using four full adder circuits connected in
series, with each full adder representing one bit position. The minuend and
subtrahend are the input signals, and the difference output is produced by the full
adders. The carry-in bit for the first full adder is set to 1, as it’s necessary for
generating the two’s complement of the subtrahend.
▪
▪ The output of each full adder is connected to the corresponding bit position in the
difference output. The carry-out bit of each full adder is connected to the carry-in
bit of the next full adder. This arrangement allows the carry bits to propagate
through the circuit, ensuring the correct subtraction operation.
IMPLEMENTATION OF THE SUBTRACTOR
USING COMBINATIONAL LOGIC GATES
▪ The full adder circuit is itself implemented using basic logic gates, such as AND,
OR, and XOR gates. Each full adder requires three XOR gates, two AND gates, and
one OR gate. Therefore, the entire 4-bit binary subtractor circuit comprises a total
of 12 XOR gates, 8 AND gates, and 4 OR gates. These gates can be interconnected
according to the full adder logic to achieve the desired subtraction operation.
▪
▪ The implementation of the subtractor circuit using combinational logic gates allows
for flexibility and customization. By choosing appropriate logic gates and their
interconnections, we can tailor the circuit to achieve specific performance
characteristics, such as minimizing gate count or optimizing delay.
EVALUATION OF THE SUBTRACTOR PERFORMANCE:
GATE COUNT, DELAY, AND POWER CONSUMPTION
▪ The performance of the 4-bit binary subtractor can be evaluated based on various
metrics, including gate count, delay, and power consumption. Gate count refers to
the number of logic gates used in the circuit. Delay represents the time it takes for
the circuit to produce a stable output after the input signals are applied. Power
consumption indicates the amount of power consumed by the circuit during
operation.
▪
▪ The gate count of our 4-bit subtractor is 24, comprising 12 XOR gates, 8 AND gates,
and 4 OR gates. The delay of the circuit is determined by the propagation delay of
the logic gates and the interconnection between them. The power consumption is
influenced by the number of gates, their switching activity, and the supply voltage.
The specific values for gate count, delay, and power consumption will vary
depending on the technology and the physical implementation of the circuit.
CIRCUIT DIAGRAM
COMPARISON TO A DEDICATED
SUBTRACTOR CIRCUIT
▪ A dedicated subtractor circuit is specifically designed to perform binary
subtraction and may utilize different logic implementations compared to our full
adder-based subtractor. Dedicated subtractor circuits may employ specialized
logic structures or techniques to optimize for specific performance characteristics.
This comparison allows us to evaluate the trade-offs associated with different
design approaches.
▪
▪ The advantage of using a dedicated subtractor circuit is that it can potentially offer
a more optimized solution in terms of gate count, delay, and power consumption.
However, the design and implementation of a dedicated subtractor can be more
complex, requiring specialized knowledge and effort. The choice between a full
adder-based subtractor and a dedicated subtractor depends on factors like
application requirements, performance goals, and available resources.
CONCLUSION AND FUTURE
CONSIDERATIONS
▪ This document has presented a comprehensive analysis of the design and
performance of a 4-bit binary subtractor using full adders and logic gates. We have
explored the principles of binary subtraction and full adder circuits, detailed the
circuit design, and evaluated the subtractor’s performance metrics. Our
comparison with a dedicated subtractor circuit has revealed the trade-offs
associated with different design approaches.
▪
▪ Further research and development can focus on optimizing the subtractor circuit’s
performance, exploring techniques like logic minimization, gate sharing, and the
use of specialized logic structures. Investigating the application of different
technologies, such as CMOS or FPGA, can also lead to improvements in gate count,
delay, and power consumption.