# binary adder

Suppose we wanted to build a device that could add two binary bits together. Such a device is known as a half-adder, and its gate circuit looks like this:

The Σ symbol represents the “sum” output of the half-adder, the sum’s least significant bit (LSB). C_{out} represents the “carry” output of the half-adder, the sum’s most significant bit (MSB).

If we were to implement this same function in ladder (relay) logic, it would look like this:

Either circuit is capable of adding two binary digits together. The mathematical “rules” of how to add bits together are intrinsic to the hard-wired logic of the circuits. If we wanted to perform a different arithmetic operation with binary bits, such as multiplication, we would have to construct another circuit. The above circuit designs will only perform one function: add two binary bits together. To make them do something else would take re-wiring, and perhaps different componentry.

In this sense, digital arithmetic circuits aren’t much different from analog arithmetic (operational amplifier) circuits: they do exactly what they’re wired to o, no more and no less. We are not, however, restricted to designing digital computer circuits in this manner. It is possible to embed the mathematical “rules” for any arithmetic operation in the form of digital data rather than in hard-wired connections between gates. The result is unparalleled flexibility in operation, giving rise to a whole new kind of digital device: the *programmable computer*.

While this chapter is by no means exhaustive, it provides what I believe is a unique and interesting look at the nature of programmable computer devices, starting with two devices often overlooked in introductory textbooks: *look-up table memories* and *finite-state machines*.

**Related**

COMMENTsongsAdder (electronics) – Wikipedia, the free encyclopedia

In electronics, an adder or summer is a digital circuit that performs addition of numbers. In modern computers adders reside in the arithmetic logic unit ( …

Although adders can be constructed for many numerical representations, such as Binary-coded decimal or excess-3, the most common adders operate on binary numbers. In …

To reduce the computation time, engineers devised faster ways to add two binary numbers by using carry lookahead adders. They …

http://en.wikipedia.org/wiki/Adder

Binary Adders using Ex-OR Gates

Electronics Tutorial about the Binary Addition of Numbers including Half and Full Binary Adders.

The Binary Adder is made up from standard AND and Ex-OR gates and allow us to “add” single bits of data together to produce two outputs, the SUM (“S”) of the addition and a CARRY (“C”). One …

By combining the Ex-OR gate with the AND gate results in a simple digital binary adder circuit known commonly as the “Half-Adder” circuit. …

http://www.electronics-tutorials.ws/combination/comb_7.html

Adding Binary Numbers

The basis of this is addition; if we can add two binary numbers, we can just as easily subtract them, or get a little fancier and perform multiplication and division. How …

We have to do the same thing with binary numbers, for the same reason. As a result, the circuit to the left is known as a “half adder,” because …

Four-bit binary adder. Now we can add two binary bits together, accounting for a possible carry from the next lower order of magnitude, and …

http://www.play-hookey.com/digital/adder.html

The binary adder

The circuit below is an adder for binary numbers encoded serially, least-significant bit first. (Fans of big-endian architectures are invited to …

bit-serial binary adder. How does it work? Just below the centre of the device is a flip-flop. This stores the current state of the carry; call …

The leftmost component of the adder is an exclusive-OR gate. This calculates A EOR B. The output of this gate goes to a (simple) AND-NOT gate just …

http://www.quinapalus.com/wires8.html

4008 4-bit binary full adder

The 4008 is a 4-bit binary full adder with two 4-bit data inputs (A0 to A3, B0 to B3), a carry input (CIN), four sum outputs (S0 to S3), and …

The simplest addition you can do is to add together two 1-bit binary numbers. Suppose the numbers are called A and B. Each of these numbers can take the values 0 or …

In other words, 1-bit binary addition can be carried out by a circuit which looks like this: half adder circuit. click for simulation Click …

http://www.doctronics.co.uk/4008.htm

Binary Adder

Binary Adder made by AND-OR Array Logic. The addition operation takes a binary input and produces a unique corresponding binary output. To make a logic circuit that performs addition …

In order make an adder using AND-OR design, we think like this. For the carry-out bit, we can look at the list we made and say: …

From this logical diagram we can create a circuit diagram for the one-bit adder. We need three inverters, which are already shown. We …

http://cpuville.com/adder.htm

Introduction to Digital Electronics – Lesson 3

A circuit that performs the addition of two binary digits like this is called a half adder (I’ll explain why we say “half” in the next section). A half adder can only add two binary digits. If you wanted a long binary number added to another long binary number, you would use several circuits ( …

We duplicate the circuit that you see above several times (8 times, 16 times or 32 times – usually a power of 2) to form a proper binary adder: …

http://richardbowles.tripod.com/dig_elec/chapter3/chapter3.htm