## Half Subtractor Truth Table

#### What is half subtractor with example?

Half Subtractor in Digital Logic – GeeksforGeeks A half subtractor is a digital logic circuit that performs binary subtraction of two single-bit binary numbers. It has two inputs, A and B, and two outputs, DIFFERENCE and BORROW. The DIFFERENCE output is the difference between the two input bits, while the BORROW output indicates whether borrowing was necessary during the subtraction.

The half subtractor can be implemented using basic gates such as XOR and NOT gates. The DIFFERENCE output is the XOR of the two inputs A and B, while the BORROW output is the NOT of input A and the AND of inputs A and B. Half subtractor is a combination circuit with two inputs and two outputs that are different and borrow,

It produces the difference between the two binary bits at the input and also produces an output (Borrow) to indicate if a 1 has been borrowed. In the subtraction (A-B), A is called a Minuend bit and B is called a Subtrahend bit. Truth Table The SOP form of the Diff and Borrow is as follows: Diff= A’B+AB’ Borrow = A’B Implementation Logical Expression Difference = A XOR B Borrow = \overline B

#### What is the output of the half subtractor?

Construction of Half Subtractor Circuit – In the block diagram, we have seen that it contains two inputs and two outputs. The carry and sum are the output states of the half subtractor. The half subtractor is designed with the help of the following logic gates:

1. 2-input AND gate.
2. 2-input Exclusive-OR Gate or Ex-OR Gate
3. NOT or inverter Gate

## Is a half subtractor using ex or gate?

Frequently Asked Questions (FAQs) – Some Frequently Asked Questions on Half Subtractor are Q1. How does a half subtractor work? Ans. A half subtractor takes two binary digits, A and B, as inputs and produces two outputs, D and B. The difference (D) output is equal to A minus B, and the borrow (B) output indicates whether a borrow is required from the next significant digit during subtraction.

Q2. How is a half subtractor implemented using gates? Ans. A half subtractor can be implemented using basic logic gates such as XOR and AND gates. The XOR gate provides the difference output, while the AND gate provides the borrow output. Q3. What is the difference between a half subtractor and a full subtractor? Ans.

A half subtractor is a digital circuit that performs subtraction of two binary digits and provides two outputs, difference and borrow. A full subtractor, on the other hand, is a digital circuit that performs the subtraction of three binary digits and provides two outputs, difference and borrow.

### What is half subtractor using NAND gates?

What is Half Subtractor? – A half-subtractor is a combinational circuit which has two inputs and two outputs where one output is difference and another is borrow bit. The half subtractor produces the difference between the two binary bits at the input and also produces a borrow output (if any). Here, A and B are the input variables (binary digits) and d is the output difference bit and b is the borrow bit. We can understand the operation of a half subtractor with the help of its truth table.

## What is half vs full subtractor?

The difference between half subtractor and full subtractor is; the output of the half subtractor is Ex-OR of two inputs. However, the difference output of the full subtractor is Ex-OR of three inputs.

#### What is difference between half subtractor and full subtractor?

Full Subtractor

The Half Subtractor is used to subtract only two numbers. To overcome this problem, a full subtractor was designed. The full subtractor is used to subtract three 1-bit numbers A, B, and C, which are minuend, subtrahend, and borrow, respectively. The full subtractor has three input states and two output states i.e., diff and borrow.

## How many NAND gates does a half subtractor have?

The number of 2-input NAND gates required to implement a 2-input XOR gate is 4.

Logic Gates Min. number of NOR Gate Min. number of NAND Gate
Half-Subtractor 5 5
Full-Subtractor 9 9

## What is the conclusion of half subtractor?

Conclusion – The half subtractor circuit is a key component of digital circuits that illustrates bit manipulation operations on binary numbers. Its straightforward but crucial architecture enables the subtraction of binary numbers, laying the groundwork for more difficult arithmetic and logic operations.

#### What are the limitations of half subtractor?

Limitation of Half Subtractor- Half subtractors do not take into account ‘Borrow-in’ from the previous circuit. This is a major drawback of half subtractors. This is because real time scenarios involve subtracting the multiple number of bits which can not be accomplished using half subtractors.

## What is SR flip flop?

SR flip-flop is a gated set-reset flip-flop. The S and R inputs control the state of the flip-flop when the clock pulse goes from LOW to HIGH, The flip-flop will not change until the clock pulse is on a rising edge. When both S and R are simultaneously HIGH, it is uncertain whether the outputs will be HIGH or LOW. Function table

#### What are the applications of subtractor?

Applications of Full Subtractor – The applications of a full subtractor are many and varied, including:

• Arithmetic circuits: Full subtractors are used in arithmetic circuits for performing binary subtraction.
• ALU (Arithmetic Logic Unit): The full subtractor is an essential component of an ALU, which performs arithmetic and logical operations in a computer’s central processing unit (CPU).
• Binary number representation: Full subtractors are used in the representation of negative binary numbers.
• Error Correction: Full subtractors are used in error correction codes for detecting and correcting errors in digital signals.
• Digital filters: Full subtractors are used in digital filters to subtract one signal from another to produce a filtered output.
• Digital clocks: Full subtractors are used in digital clocks to subtract one number from another to obtain the elapsed time.
• Microcontrollers: Full subtractors are used in microcontrollers to perform subtraction operations as part of their instruction set.
• Digital signal processing: Full subtractors are used in digital signal processing to perform subtraction operations on signals.

So, the full subtractor is a versatile combinational logic circuit that is widely used in various digital systems and applications. It is used in arithmetic circuits, ALUs, error correction, digital filters, digital clocks, microcontrollers, and digital signal processing, among others.

1. Conclusion In conclusion, the full subtractor is a useful digital logic circuit that performs binary subtraction of two numbers while taking into account borrowing from a previous subtraction.
2. It has three inputs and two outputs.
3. The full subtractor circuit is widely used in various digital systems and applications, such as arithmetic circuits, ALUs, error correction codes, digital filters, digital clocks, microcontrollers, and digital signal processing, among others.

The full subtractor is a simple, yet versatile digital logic circuit that plays a crucial role in many digital systems and applications. It is an essential component in digital arithmetic and has the ability to perform binary subtraction with borrowing, making it an important component in digital systems that require binary arithmetic operations.

#### What is the difference between a half adder and a half subtractor?

However, a half adder is used to add two single-bit binary numbers (sum and carry), while a half subtractor is used to subtract two single-bit binary numbers (difference and borrow). A half adder takes two input bits and produces two output bits, a sum bit and a carry bit.

## What is 2 bit subtractor?

2 bit Full Subtractors – A full Subtractor works really well in the processor. We’ll talk about it function but before that have a look at its definition:

• 2 bit Full Subtractor is a Combinational Logic that contain three Inputs and Two outputs and perform the function of Subtraction with two bits,
• Minuend: The 1st input is called the Minuend used to take the bit from which the 2nd value will be Subtracted.
• Subtrahend : It is called the 2nd input that is subtracted from Minuend.
• Borrow in: It is the third input that is use to take the value of the Previous borrow and we’ll denote it as B(in) here.
• Borrow Out: The Borrow out is symbolized as B(out) and it the resultant borrow that the output Terminal shows.
• Difference: This is the main result that was the concern of the experiment and its value totally depends upon the binary subtraction rules.

#### What is a subtractor in logic?

Conclusion – From the above discussion, we can conclude that a full-subtractor is a combinational logic circuit that can compute the difference of three binary digits. In a full subtractor, the borrow (if any) from the previous stage is also used in subtraction operation in the next stages. : Full Subtractor in Digital Electronics

### What are the advantages of half subtractor?

The advantages of half subtractor are: The implementation and construction of this circuit is simple and easy. This circuit consumes minimal power in digital signal processing. computational functionalities can be performed at improved speed rates.

### What are the two inputs of half subtractor?

1) Half Subtractor – The half-subtractor is a combinational circuit which is used to perform subtraction of two bits. It has two inputs, A (minuend) and B (subtrahend) and two outputs Difference and Borrow. The logic symbol and truth table are shown below. Figure-1:Logic Symbol of Half subtractor Figure-2:Truth Table of Half subtractor Figure-3:Circuit Diagram of Half subtractor From the above truth table we can find the boolean expression. Difference = A ⊕ B Borrow = A’ B From the equation we can draw the half-subtractor circuit as shown in the figure 3.

### What are the applications of half and full subtractor?

Difference Between Half Subtractor and Full Subtractor –

 Half Subtractor Full Subtractor It is a type of combinational logic circuit that subtracts two binary digit of one bit each and provides output in the form of difference and borrow. It is a type of combinational logic circuit that subtracts three binary digits of one bit each and provides output on the form of difference and borrow. It does not add the borrow obtained from previous subtraction to the next subtraction. It subtracts the borrow obtained from A, B to C. A half subtractor circuit is designed using only one AND gate, NOT gate and XOR gate. A full subtractor circuit is designed using two XOR gate, two NOT gate, two AND gate and one OR gate. Half subtractor has two inputs Full subtractor has 3 inputs Half subtractor is used in digital measuring devices and calculators, etc. Full subtractor is used in digital processors and subtraction of multiple bits, etc. The logic expression for half subtractor is given as Difference ( D ) = A’B + AB’ = A ⊕ B Borrow ( Br ) = A’B The logic expression for full subtractor is given as Difference ( D ) = A ⊕ B ⊕ C Carry = A’B + BC + A’C

## What is half adder truth table?

Half Adder Truth Table – To obtain the relation of the output obtained to the applied input can be analyzed using a table known as Truth Table. Half Adder Truth Table From the above truth table the points are evident as follows:

• If A=0, B=0 that is both the inputs applied are 0. Then both the outputs SUM and CARRY are 0.
• Among two inputs applied if anyone the input is 1 then the SUM will b e1 but the CARRY is 0.
• If both the inputs are 1 then the SUM will be equal to 0 and the CARRY will be equal to 1.

Based on the inputs applied the half adder proceeds with the operation of addition.

## What is the truth table of multiplexer?

4-to-1 Multiplexer – A 4-to-1 multiplexer consists four data input lines as D0 to D3, two select lines as S0 and S1 and a single output line Y. The select lines S0 and S1 select one of the four input lines to connect the output line. The figure below shows the block diagram of a 4-to-1 multiplexer in which, the multiplexer decodes the input through select line.

 S0 S1 D0 D1 D2 D3 Y X X X 1 X X X 1 1 X X X 1 X 1 X X 1 1 X X X 1 X X 1 X 1 1 1 X X X 1 1 X X X 1 1

From the above truth table, we can write the output expressions as follows: Y = S0 S1 D0 + S0 S1 D1 + S0 S1 D2 + S0 S1 D3 From the above expression of the output, a 4-to-1 multiplexer can be implemented by using basic logic gates. The below figure shows the logic circuit of 4:1 MUX which is implemented by four 3-inputs AND gates, two 1-input NOT gates, and one 4-inputs OR gate.

1. In this circuit, each data input line is connected as input to an AND gate and two select lines are connected as other two inputs to it.
2. Additionally, there is also an Enable Signal.
3. The output of all the AND gates are connected to inputs of OR gate in order to produce the output Y.
4. Generally, this type of multiplexers is available in IC with dual mode i.e., there will be two 4-to-1 Multiplexers in a single IC.

The most common and popular 4-to-1 line multiplexer is IC 74153 which, is a dual 4-to-1 line multiplexer. It consists of two identical 4-to-1 multiplexers. It has two separate enable or strobe inputs to switch ON or OFF the individual multiplexers. But the Select lines are common to both the Multiplexers.

### What is the truth table for boolean identities?

5.3.5 Truth Tables – The truth table displays the logical operations on input signals in a table format. Every Boolean expression can be viewed as a truth table. The truth table identifies all possible input combinations and the output for each. It is common to create the table so that the input combinations produce an unsigned binary up-count.

• The truth table for the AND gate is shown in Table 5.13,
• Here, the output Z is a logic 1 only when both inputs A and B are logic 1.
• Table 5.13,
• AND gate truth table The truth table for the NAND gate is shown in Table 5.14,
• Here, the output Z is a logic 0 only when both inputs A and B are logic 1.
• This is the logical inverse of the AND gate.

Table 5.14, NAND gate truth table The truth table for the OR gate is shown in Table 5.15, Here, the output Z is a logic 1 when either or both inputs A and B are logic 1. Table 5.15, OR gate truth table The truth table for the NOR gate is shown in Table 5.16,

1. Here, the output Z is a logic 0 when either or both inputs A and B are logic 1.
2. This is the logical inverse of the OR gate.
3. Table 5.16,
4. NOR gate truth table The truth table for the EX-OR gate is shown in Table 5.17,
5. Here, the output Z is a logic 1 when either but not both inputs A and B are logic 1.
6. Table 5.17,

EX-OR gate truth table The truth table for the EX-NOR gate is shown in Table 5.18, Here, the output Z is a logic 0 when either but not both inputs A and B are logic 1. This is the logical inverse of the EX-OR gate. Table 5.18, EX-NOR gate truth table The truth table for the NOT gate (inverter) is shown in Table 5.19,

This gate has one input only. The output Z is the logical inverse of the input A. Table 5.19, NOT gate truth table The truth table for the BUFFER is shown in Table 5.20, This gate has one input only. The output Z is the same logical value as that of the input A. Table 5.20, BUFFER truth table Another way to describe a digital circuit or system is by using a suitable HDL such as VHDL,

This describes the operation of the circuit or system at different levels of design abstraction. An example VHDL description for each of the basic logic gates using the built-in logical operators in VHDL is shown in Figure 5.10, The syntax and semantics of the language will be provided in Chapter 6, Figure 5.10, VHDL code examples for the logic gates in Figure 5.8 The EX-OR gate has the Boolean expression: Z = A ⊕ B From the truth table for the EX-OR gate, then, a Boolean expression in the first canonical form (the first canonical from is a set of minterms that are AND logical operators on the variables within the expression with the output of the AND logical operators being logically ORed together) can be written as: Z = ( A ¯,B ) + ( A, Figure 5.11, EX-OR gate using discrete logic gates The truth table can be created to identify the input-output relationship for any logic circuit that consists of combinational logic gates and that can be expressed by Boolean logic. It is therefore possible to move between Boolean logic expressions and truth tables.

• Consider a three-input logic circuit (A, B, and C) with one output (Z), as shown in the truth table in Table 5.21,
• The inputs are written as a binary count starting at 0 10 and incrementing to 7 10,
• The output Z is only a logic 1 when inputs A, B, and C are logic 1.
• This can be written as a Boolean expression Table 5.21,

Three-input logic circuit truth table: Z = A.B.C

A B C Z
1
1
1 1
1
1 1
1 1
1 1 1 1

Z = A,B,C Here, where the output Z is a logic 1, the values of inputs A, B, and C are ANDed together. Where a variable is a logic 1, then the variable is used. When the variable is a logic 0, then the inverse (NOT) of the variable is used. Consider now another three-input logic circuit (inputs A, B, and C) with one output (Z), shown in Table 5.22,

A B C Z
1
1
1
1 1
1
1 1
1 1
1 1 1

Z = A ¯, B ¯, C ¯ Here, where the output Z is a logic 1, the values of inputs A, B, and C are ANDed together. Where a variable is a logic 1, then the variable is used. When the variable is a logic 0, then the inverse (NOT) of the variable is used. The expression identified for the truth table in Table 5.22 can be modified using rules and laws identified in Table 5.12 : Z = A ¯,

• B ¯, C ¯ Z = A ¯, B ¯,
• C ¯ ¯ Z = A ¯ ¯, B ¯ ¯,
• C ¯ ¯ ¯ Z = A + B + C ¯ The original expression was manipulated by first double-inverting the expression (which logically makes no change), then breaking one of the inversions (the inversion closest in space to the variables) and changing the AND operator to an OR operator (the second De Morgan theorem).

This leaves a NOR expression with double-inverted variables. The double-inversion on each input is then dropped. Now, combining the operations in Table 5.21 and Table 5.22 produces a more complex operation as shown in Table 5.23, Table 5.23, Three-input logic circuit truth table: complex logic gate

A B C Z
1
1
1
1 1
1
1 1
1 1
1 1 1 1

The Boolean expression for this is: Z = ( A,B,C ) + ( A ¯ + B ¯ + C ¯ ) Each of the ANDed expressions is ORed together. Parentheses group each expression to aid readability of the expression. In this form of expression, the first canonical form, a set of minterms (minimum terms) that are AND logical operators are created (one for each line of the truth table where the output is a logic 1). Figure 5.12, Circuit schematic for Boolean expression in Table 5.23 The second canonical form is an alternative to the first canonical form. In the second, a set of maxterms that are OR logical operators on the variables within the expression are created (one for each line of the truth table where the output is a logic 0).