# 3 bit binary adder circuit

Each horizontal line represents a multiple-input OR operation that has as its inputs the outputs of the operations from the AND plane above. In the diagram above, the outputs of the first four AND operations serve as inputs to a 4- input OR operation, the output of which is the Sum bit. From this logical diagram we can create a circuit diagram for the one-bit adder.

We need three inverters, which are already shown. You have seen that we may use two two-input AND gates to make a single three-input gate, so we will need 13 two-input AND gates total. We need three two-input OR gates to make a single four-input OR gate for the sum bit, and two more for the three-input OR for the carry-out bit, so we need 5 two-input OR gates in all. This AND operation is seen in both the second and fifth columns, labeled as 1 in the figure below, so we need only one two-input AND gate for this instead of two.

The output this one gate can be sent to the inputs of both of the second AND gates to finish the operations. Now we only need a total of 10 two-input AND gates for the complete adder circuit. Here is a circuit diagram of the adder. The three AND gates that are used twice are also labeled below. The circuit has one noticeable flaw. The inputs are each connected to several gates, meaning that the adder will appear to draw more current than a single standard input.

This is easily corrected by adding a non-inverting buffer at each input. Then, the adder inputs will appear to be the same as the inputs of any other logic gate. In fact, we can use a symbol for the adder just as we would for the logic gates. Like the other logic gate circuits, the power supply inputs are not shown, but understood to be present.

The basic adder circuit shown above is able to add only two one-bit numbers and a carry. However, these one-bit adders, like other logic circuits, are designed so that they can be connected together in networks. When combined as pictured below, we can easily make a circuit that will add two 4-bit binary numbers. We can make an 8-bit adder from two four-bit adders, and so on to make a circuit that can add numbers of any size. You have seen how complex circuits can be made of NAND gates.

In fact, any circuit that takes a binary input and has a corresponding binary output can be made the same way. Projects Projects home Z80 wire wrap Original processor 8-bit processor. A one-bit full-adder adds three one-bit numbers, often written as A , B , and C in ; A and B are the operands, and C in is a bit carried in from the previous less-significant stage.

The circuit produces a two-bit output. A full adder can be implemented in many different ways such as with a custom transistor -level circuit or composed of other gates. In this implementation, the final OR gate before the carry-out output may be replaced by an XOR gate without altering the resulting logic.

Using only two types of gates is convenient if the circuit is being implemented using simple IC chips which contain only one gate type per chip.

Assumed that an XOR-gate takes 1 delays to complete, the delay imposed by the critical path of a full adder is equal to. It is possible to create a logical circuit using multiple full adders to add N -bit numbers. Each full adder inputs a C in , which is the C out of the previous adder.

This kind of adder is called a ripple-carry adder , since each carry bit "ripples" to the next full adder. The layout of a ripple-carry adder is simple, which allows fast design time; however, the ripple-carry adder is relatively slow, since each full adder must wait for the carry bit to be calculated from the previous full adder.

The gate delay can easily be calculated by inspection of the full adder circuit. Each full adder requires three levels of logic. The carry-in must travel through n XOR-gates in adders and n carry-generator blocks to have an effect on the carry-out. To reduce the computation time, engineers devised faster ways to add two binary numbers by using carry-lookahead adders.

They work by creating two signals P and G for each bit position, based on whether a carry is propagated through from a less significant bit position at least one input is a 1 , generated in that bit position both inputs are 1 , or killed in that bit position both inputs are 0.

In most cases, P is simply the sum output of a half adder and G is the carry output of the same adder.

After P and G are generated, the carries for every bit position are created. Some other multi-bit adder architectures break the adder into blocks. It is possible to vary the length of these blocks based on the propagation delay of the circuits to optimize computation time.

These block based adders include the carry-skip or carry-bypass adder which will determine P and G values for each block rather than each bit, and the carry select adder which pre-generates the sum and carry values for either possible carry input 0 or 1 to the block, using multiplexers to select the appropriate result when the carry bit is known. By combining multiple carry-lookahead adders, even larger adders can be created.

This can be used at multiple levels to make even larger adders. Other adder designs include the carry-select adder , conditional sum adder , carry-skip adder , and carry-complete adder. If an adding circuit is to compute the sum of three or more numbers, it can be advantageous to not propagate the carry result.

Instead, three-input adders are used, generating two results: The sum and the carry may be fed into two inputs of the subsequent 3-number adder without having to wait for propagation of a carry signal.

After all stages of addition, however, a conventional adder such as the ripple-carry or the lookahead must be used to combine the final sum and carry results. We can view a full adder as a 3: