A binary adder-subtractor is a digital circuit that can do **both addition** and subtraction of binary values in the same circuit. The operation is determined by the binary value of the control signal. Because we're working with 4-bit numbers, the circuit has four complete adders. Each 4-bit number is added to all the other 3-bit numbers. Then each pair of bits is subtracted from the third bit. The result is a sum for **each set** of equivalent bits (000 - 111), a carry out for **each 1-bit difference** (100 - 110), and a control signal to determine if a subtraction should occur.

The truth table shows all combinations of inputs and outputs. For example, when input A is 0 and B is 1, output C will be 1. When input A is 1 and B is 0, output C will be 0. If either or both inputs are not equal to 0 or 1, then output C will remain at its current value of A + B + D.

Adders-subtractors are useful for removing intermediate results from sums or subtractions. They can also reduce the number of pins on an integrated circuit by combining several bits into a single output pin. Finally, they can be used as a partial register by setting the control signal to subtract rather than add. This will keep only the lowest order bit of the output changed by each calculation.

An adder-subtractor is a circuit in digital circuits that can add or subtract integers (in particular, binary). The circuit below adds or subtracts based on a control signal. It is also feasible to build a circuit that conducts **both addition** and subtraction simultaneously. Adders and subtractors are important logic gates for constructing **more complex logic functions**.

As shown in the figure above, an adder-subtractor has two input terminals and one output terminal. When the control signal at the gate terminal is low, the output is equal to the sum of the inputs; when the control signal is high, the output is equal to the difference of the inputs. This type of circuit can be used as a module within larger circuits. For example, it can be used as a component in a binary multiplier or binary divider circuit.

Adders and subtractors can be constructed using standard logic components such as NOR gates, NAND gates, and XOR gates. These basic components are described in more detail below.

Adders and subtractors can also be constructed using multiplexers. A multiplexer is a circuit that allows you to choose between several inputs and provide them all to **only one output**. In other words, it can "select" one input from among **several possible inputs**.

A single binary adder may execute both addition and subtraction operations. Such a binary circuit may be built by coupling **an Ex-OR gate** with each complete adder, as illustrated in the picture below. The image below depicts a 4-bit parallel binary adder/subtractor with two 4-bit inputs labeled 'A3 A2 A1 A0' and 'B3 B2 B1 B0'.

The output of the first EX-OR gate is connected to the input of **the second EX-OR gate**. The output of the second EX-OR gate is the result of the addition operation. The output of the first EX-OR gate is used as a carry input for the next higher bit position.

Binary arithmetic circuits are often constructed from basic building blocks, such as full adders and half adders. A full adder adds two n-bit numbers and produces a result that is equal to either of **the two input numbers**. If the output of the full adder is to be interpreted as a n-bit number, then it must be truncated to n bits before being used as a component in another adder or multiplier circuit. Half adders are equivalent to full adders but operate on only one of its inputs at a time. They can be used instead of dividers to reduce **high-order terms** in a division problem to yield the quotient and remainder simultaneously.

Binary arithmetic circuits are commonly used to implement computers and other logic devices. Full adders and half adders can also be used separately to perform specific tasks.

A subtraction machine An electronic logic circuit used to compute the difference between **two binary values**, the minuend and the number to be subtracted, the subtrahend (see table). This computation is performed using **a complete subtractor**, which has three inputs: a minuend bit, a subtrahend bit, and a borrow bit. The output of a complete subtractor is a negative indication of whether or not there was a carry out during **the subtraction process**.

The term "subtractor" can also be applied to an individual full-adder circuit. In this case, the three-input device is called a "subtractor gate".

In modern electronics, a subtracter circuit is usually implemented as an integrated circuit (IC), but it could also be constructed using discrete components. For example, one might construct a simple subtracter using bipolar junction transistors (BJTs) or field effect transistors (FETs).

The first subtractors were built from vacuum tubes, especially in military applications. They were later replaced by **electronic circuits** based on silicon transistors. Today, most computers include **at least one embedded subtracter circuit**. It is often required for arithmetic operations such as addition and multiplication.

Subtractors are commonly found in engineering workstations, personal computers, and video games. They are also useful for reducing errors caused by counting mistakes.