## Full Subtractor Truth Table

Contents

- 1 What is the full subtractor truth table?
- 2 What is the full subtractor theory?
- 3 What is a 3 bit full subtractor?
- 4 What is full subtractor using NAND gate?
- 5 How many NAND gates does a full subtractor need?
- 6 Where is full subtractor used?
- 7 What is a full subtractor circuit using multiplexers?
- 8 What is 2 bit full subtractor?
- 9 What is the conclusion of half subtractor AND full subtractor?
- 10 What is full adder subtractor?

## What is the full subtractor truth table?

Full Subtractor Truth Table – This subtractor circuit executes a subtraction between two bits, which has 3- inputs (A, B, and Bin) and two outputs (D and Bout). Here the inputs indicate minuend, subtrahend, & previous borrow, whereas the two outputs are denoted as borrow o/p and difference. The following image shows the truth table of the full-subtractor.

Inputs | Outputs | |||

Minuend (A) | Subtrahend (B) | Borrow (Bin) | Difference (D) | Borrow (Bout) |

0 | 0 | |||

0 | 1 | 1 | 1 | |

1 | 1 | 1 | ||

1 | 1 | 1 | ||

1 | 1 | |||

1 | 1 | 0 | ||

1 | 1 | |||

1 | 1 | 1 | 1 | 1 |

## What is the full subtractor theory?

Full Subtractor in Digital Logic A full subtractor is a combinational circuit that performs subtraction of two bits, one is minuend and other is subtrahend, taking into account borrow of the previous adjacent lower minuend bit. This circuit has three inputs and two outputs,

The three inputs A, B and Bin, denote the minuend, subtrahend, and previous borrow, respectively. The two outputs, D and Bout represent the difference and output borrow, respectively. Although subtraction is usually achieved by adding the complement of subtrahend to the minuend, it is of academic interest to work out the Truth Table and logic realisation of a full subtractor; x is the minuend; y is the subtrahend; z is the input borrow; D is the difference; and B denotes the output borrow.

The corresponding maps for logic functions for outputs of the full subtractor namely difference and borrow. Here’s how a full subtractor works: 1. First, we need to convert the binary numbers to their two’s complement form if we are subtracting a negative number.2. Next, we compare the bits in the minuend and subtrahend at the corresponding positions. If the subtrahend bit is greater than or equal to the minuend bit, we need to borrow from the previous stage (if there is one) to subtract the subtrahend bit from th e minuend bit.3.

We subtract the two bits along with the borrow-in to get the difference bit. If the minuend bit is greater than or equal to the subtrahend bit along with the borrow-in, then the difference bit is 1, otherwise it is 0.4. We then calculate the borrow-out bit by comparing the minuend and subtrahend bits.

If the minuend bit is less than the subtrahend bit along with the borrow-in, then we need to borrow for the next stage, so the borrow-out bit is 1, otherwise it is 0.

- The circuit diagram for a full subtractor usually consists of two half-subtractors and an additional OR gate to calculate the borrow-out bit. The inputs and outputs of the full subtractor are as follows:
- Inputs :
- A: minuend bitB: subtrahend bitBin: borrow-in bit from the previous stage
- Outputs :
- Diff: difference bitBout: borrow-out bit for the next stage
- Truth Table –

From above table we can draw the K-Map as shown for “difference” and “borrow”. Logical expression for difference – D = A’B’Bin + A’BBin’ + AB’Bin’ + ABBin = Bin(A’B’ + AB) + Bin'(AB’ + A’B) = Bin( A XNOR B) + Bin'(A XOR B) = Bin (A XOR B)’ + Bin'(A XOR B) = Bin XOR (A XOR B) = (A XOR B) XOR Bin Logical expression for borrow – Bout = A’B’Bin + A’BBin’ + A’BBin + ABBin = A’B’Bin +A’BBin’ + A’BBin + A’BBin + A’BBin + ABBin = A’Bin(B + B’) + A’B(Bin + Bin’) + BBin(A + A’) = A’Bin + A’B + BBin OR Bout = A’B’Bin + A’BBin’ + A’BBin + ABBin = Bin(AB + A’B’) + A’B(Bin + Bin’) = Bin( A XNOR B) + A’B = Bin (A XOR B)’ + A’B Logic Circuit for Full Subtractor – Implementation of Full Subtractor using Half Subtractors – 2 Half Subtractors and an OR gate is required to implement a Full Subtractor.

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: Full Subtractor in Digital Logic

## What is a 3 bit full subtractor?

2) Full Subtractor – A full subtractor is a combinational circuit that performs subtraction involving three bits, namely A (minuend), B (subtrahend), and Bin (borrow-in), It accepts three inputs: A (minuend), B (subtrahend) and a Bin (borrow bit) and it produces two outputs: D (difference) and Bout (borrow out). The logic symbol and truth table are shown below. Figure-4:Logic Symbol of Full subtractor Figure-5:Truth Table of Full subtractor From the above truth table we can find the boolean expression. D = A ⊕ B ⊕ Bin Bout = A’ Bin + A’ B + B Bin From the equation we can draw the Full-subtractor circuit as shown in the figure 6. Figure-6:Circuit Diagram of Full subtractor

#### What logic gates are used in full subtractor?

Construction of Full Subtractor Circuit: – The above block diagram describes the construction of the Full subtractor circuit, In the above circuit, there are two half adder circuits that are combined using the OR gate. The first half subtractor has two single-bit binary inputs A and B. As we know that, the half subtractor produces two outputs, i.e., ‘Diff’ and ‘Borrow’.

- The ‘Diff’ output of the first subtractor will be the first input of the second half subtractor, and the ‘Borrow’ output of the first subtractor will be the second input of the second half subtractor.
- The second half subtractor will again provide ‘Diff’ and ‘Borrow’.
- The final outcome of the Full subtractor circuit is the ‘Diff’ bit.

In order to find the final output of the ‘Borrow’, we provide the ‘Borrow’ of the first and the second subtractor into the OR gate. The outcome of the OR gate will be the final carry ‘Borrow’ of full subtractor circuit. The MSB is represented by the final ‘Borrow’ bit. The actual logic circuit of the full subtractor is shown in the above diagram. The full subtractor circuit construction can also be represented in a Boolean expression.

## What is full subtractor using NAND gate?

Realization of a Full Subtractor using NAND gate In digital electronics, a subtractor is a combinational logic circuit that performs the subtraction of two binary numbers. However, the subtraction of binary number can be performed using adder circuits by taking 1s or 2s compliments.

- But, we may also realize a dedicate circuit to perform the subtraction of two binary numbers.
- In the subtraction of two binary numbers, each subtrahend bit of the number is subtracted from its corresponding significant minuend bit to form a difference bit.
- During the subtraction, if the minuend bit is smaller than the subtrahend bit, then a 1 is borrowed from the next position.

Depending upon the number of bits taken as input, there are two types of subtractors namely, Half Subtractor and Full Subtractor, A half subtractor is one that takes two binary digits as input and gives a difference bit and a borrow bit (if any) as output.

On the other hand, a full subtractor is one that takes three bits as input, i.e. two are the input bits and one is the input borrow bit from the previous stage, and gives a difference bit and a output borrow bit as the output. Since a subtractor is a combinational logic circuit, i.e. it is made of logic gates.

We can realize a full adder circuit using different types of logic gates like AND, OR, NOT, NAND, NOR, etc. In this article, we will discuss the realization of a full subtractor using NAND gates. But before that let’s have a look into the basics of full subtractor.

## How many NAND gates does a full subtractor need?

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-Adder | 5 | 5 |

Half-Subtractor | 5 | 5 |

Full-Adder | 9 | 9 |

Full-Subtractor | 9 | 9 |

#### What is full subtractor and full adder?

A full subtractor is a combinational circuit that performs the subtraction of two binary digits, taking into account the borrow from the previous subtraction. On the other hand, a full adder is a combinational circuit that adds three binary digits, including a carry-in from the previous edition.

#### What are the advantages of full subtractor?

Cascading Subtractor Circuits – As of now, we described the construction of single bit full-Subtractor circuit with logic gates. But what if we want to subtract two, more than one bit numbers? Here is the advantage of full Subtractor circuit. We can cascade single bit full Subtractor circuits and could subtract two multiple bit binary numbers. In such cases a cascaded full-Adder circuit can be used with NOT gates. We could use 2’s compliment method and it is popular method to convert a full adder circuit to a full Subtractor. In such case, we generally invert the Logic of subtrahend inputs of the full adder by inverter or NOT gate.

- By adding this non inverted input (Minuend) and Inverted Input (Subtrahend), while the carry input (LSB) of the full adder circuit is in Logic High or 1, we subtract those two binaries in 2’s complement method.
- The output from the Full-adder (which is now full Subtractor) is the Diff bit and if we invert the carry out we will get the Borrow bit or MSB.

We can actually construct the circuit and observe the output.

#### What is a 4-bit subtractor?

The 4-bit adder-subtractor is a digital circuit capable of performing arithmetic operations on binary numbers of four bits in length.

#### What is 8 bit subtractor?

The 8-bit binary adder/subtractor is a combinational circuit which performs arithmetic operations, i.e. addition and subtraction, with binary digits. In this paper, we have designed a hierarchical circuit. First, a half adder was designed based on majority gate in which the full adder was developed.

## Where is full subtractor used?

Applications of Full Subtractor – The following are some important applications of full subtractor −

- Full subtractors are used in ALU (Arithmetic Logic Unit) in computers CPUs.
- Full subtractors are extensively used to perform arithmetical operations like subtraction in electronic calculators and many other digital devices.
- Full subtractors are used in different microcontrollers for arithmetic subtraction.
- They are used in timers and program counters (PC).
- Full subtractors are also used in processors to compute addresses, tables, etc.
- Full subtractors are also used in DSP (Digital Signal Processing) and networking based systems.

### What logic gate is most used?

Basic logic gate and circuit types – There is a variety of standard building blocks or basic types of logic gate that can be used.

Buffer: Possibly not a proper type of logic gate in the strict sense, but sometimes a gate may be introduced to act as a buffer for a variety of reasons. Logic buffer gate symbol Sometimes buffers may be introduced to give a higher output capability, to speed up the edge of a logic signal, or sometimes to add a small delay. In view of this, buffers are more widely used than might be expected at a first glance. Logic inverter circuit symbol The NOT logic gate is an invaluable type of gate that is extensively used in logic circuits. Often two gates together may be used when no inversion is required but a small delay is needed. This technique can work when no buffers are present. Logic AND gate circuit symbol Logic NAND gate circuit symbol The AND and NAND gates are possibly the most widely used form of logic gate that are used. Of the two the NAND gate is the most widely seen. OR / NOR : OR gates and NOR gates are another form of logic gate that form one of the basic building blocks of digital technology. Logic OR gate circuit symbol Logic NOR gate circuit symbol Like the NAND gate, the NOR gate is the more widely used of this pair of logic gates. Exclusive OR / NOR: An exclusive OR or NOR type of logic gate is used where an output change is only required where one or the other input is high and not both. Logic Exclusive OR gate circuit symbol Logic Exclusive NOR gate circuit symbol Although the more familiar standard type of OR or NOR gate is more widely used, there are some circumstances where the exclusive OR or NOR is required. RS Flip-Flop: The initials of the RS flip flop stand for Set-Reset. This type of logic gate or circuit has two inputs, the set and reset. As might be expected, this type of logic circuit is set when one input is triggered and reset when the other is triggered. Read more about the RS Flip Flop D-Type Flip Flop: The D-Type flip flop could be termed as a form or type of logic circuit. It is a form of flip flop that transfers the input data to the output on the edge of the clock signal. It is a particularly useful form of flip flop that finds many uses in a variety of applications. J-K Flip Flop: The J-K flip-flop is the most versatile of the basic flip-flops and it can be configured to operate in a variety of modes. Counter: Counters are widely used in various forms of logic circuit. Essentially they take in a train of pulses and dependent upon their division ratio, the output a pulse after a set number of pulses have entered.

More Digital Logic and Embedded Topics: FPGA programming Embedded systems How a computer works Logic circuit design basics Logic / circuit design guidelines Return to Digital / Logic / Processing menu,,

## What is a full subtractor circuit using multiplexers?

Full subtractor using multiplexer. A full subtractor is a combinational logic circuit. It has three inputs ( each of one bit ) termed as A, B and C in that generates difference ( D ) and borrow ( B r ) in the output. A full subtractor circuit is designed using two AND gate, two NOT gate, two XOR gate, and one OR gate.

- The XOR gate gives the output for difference and the OR gate gives the output for borrow.
- In this article I will show you how can you implement full subtractor using multiplexer.
- The implementation of full subtractor in 4:1 and 8:1 multiplexer is explained with truth table, conversion & circuit diagram.

Truth table for full subtractor is shown below. This truth table is written by the concept of binary subtraction. That is 0 – 0 = 0 1 – 0 = 1 0 – 1 = 1, borrow = 1 1 – 1 = 0

A | B | C in | Difference | Borrow |

0 | 0 | 0 | 0 | 0 |

0 | 0 | 1 | 1 | 1 |

0 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 0 | 1 |

1 | 0 | 0 | 1 | 0 |

1 | 0 | 1 | 0 | 0 |

1 | 1 | 0 | 0 | 0 |

1 | 1 | 1 | 1 | 1 |

## What is 2 bit full 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.

### Why is NAND gate preferred?

From Wikipedia, the free encyclopedia

NAND gate truth table | ||
---|---|---|

Input | Output | |

A | B | A NAND B |

1 | ||

1 | 1 | |

1 | 1 | |

1 | 1 | 0 |

MIL/ANSI Symbol IEC Symbol DIN Symbol In digital electronics, a NAND gate ( NOT-AND ) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate, A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results.

- A NAND gate is made using transistors and junction diodes.
- By De Morgan’s laws, a two-input NAND gate’s logic may be expressed as A • B = A + B, making a NAND gate equivalent to inverters followed by an OR gate,
- The NAND gate is significant because any boolean function can be implemented by using a combination of NAND gates.

This property is called functional completeness, It shares this property with the NOR gate, Digital systems employing certain logic circuits take advantage of NAND’s functional completeness. NAND gates with two or more inputs are available as integrated circuits in transistor-transistor logic, CMOS, and other logic families,

#### What is the difference between half AND 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.

### How many NAND gates are required for half subtractor?

Half Subtractor Using NAND Gates – We may implement the logic circuit of half subtractor using NAND gates only as shown in figure-2. From this logic circuit diagram, we can see that 9 NAND gates are required for realization of the half subtractor. The output equations of the half subtractor in NAND logic are as follows − Difference Bit (d) $$\mathrm }\cdot \overline }}=A\oplus B}$$ Borrow Bit (b) $$\mathrm }}=\overline B}$$ In this way, we can realize the half subtractor using the NAND gates only.

## What is the conclusion of half subtractor AND full subtractor?

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 the truth table of half subtractor?

Truth Table of Half Subtractor

Inputs | Outputs | |
---|---|---|

A | B | d (Difference) |

1 | 1 | |

1 | 1 |

#### What is the truth table for a full adder?

Truth Table of Full Adder

Inputs | Outputs | |
---|---|---|

1 | 1 | |

1 | ||

1 | 1 | |

1 | 1 | 1 |

### What is a full subtractor and half 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 full adder subtractor?

Conclusion – In this tutorial, we discussed in detail about adders and subtractors in digital electronics. We may conclude the above discussion in the following points −

- A combinational logic circuit which is designed to add two binary digits is called as a half adder.
- A combinational logic circuit that can add two binary digits (bits) and a carry bit, and produces a sum bit and a carry bit as output is known as a full-adder.
- A half-subtractor is a combinational logic circuit that have two inputs and two outputs (i.e. difference and borrow).
- A full-subtractor is a combinational circuit that has three inputs A, B, bin and two outputs d and b.

Both adders and subtractors are the crucial logic circuits in arithmetic logic units of microprocessors and microcontrollers. This is because, they perform the two most basic arithmetic operations, i.e., addition and subtraction of binary numbers. Another important point to note about the adder and subtractor is that they both are the combinational logic circuits, i.e., their outputs depend on the present inputs only, but not on the past history. : Adders and Subtractors in Digital Electronics