Four Bit Carry Adder/Subtractor Circuit

After creating my 1 bit full adder design found in a previous post, I decided to go for something a little more complicated. I wanted to prove to myself that the ripple carry system worked, so the obvious choice is to make a multi bit device. 4 bits seemed like a good amount, it’s a value used in some early ALU’s so it can be used in a future project. To make it more interesting I added in the ability to make the device a Subtractor at the same time. When you look at the schematic, it only requires one more device per adder, so it’s not even an expensive thing to implement, but adds lots of functionality. As with the 1 bit adder, I have attempted to build this adder using only single logic chips.

4 bit adder-subtractor circuit

The first stage is to know the logic circuit, its widely known and can be found pretty easily all over the web. I’m not going to explain how it’s created (I can always make a separate post on that) but I can describe how to use it. The aim is for the device to take two 4 bit inputs (0 – 15), along with a carry from another adder. So the adder needs to be able to output a value between 0 and 31. In binary this can be shown as 5 bits, so we have 2 outputs. This the S output is a 4 bit bus, and the Co output bumps this up to the 5 bits we need to make 31. A truth table can be made for this but it would be 32 lines long, so too much for this post. You could regard it as a personal challenge if you want to attempt it on your own.

So I got onto Altium and made a schematic of this circuit using some of the low voltage 7400 LVC series individual logic gates that I used on the previous adder I made. They come in SOT23-5 packages which are leaded a nice size to solder. Plus they are a size where it’s possible to probe the pins fairly easily. Luckily Altium shows the components as their logic symbols. Below I have shown the first two adders, the third and fourth are basically the same as the second one, which is the idea of the ripple carry adder.

The first two adders of the four found on the board

I also added a few LEDs to show what parts are on and off. This means the user can see the inputs and outputs. These LEDs run off the 5V input voltage, and have 220Ω current limiting resistors in series with them. Also, I have put in some 0.1 inch header pins so it can be attached into a breadboard and maybe even a micro.

The LEDs for the carry bits and outputs
The LEDs for the input bits

As a base of my circuit, I have decided on a double sided 100mm x 100mm board. This is quite big as you can see for the circuit I have made, but gives plenty of space for a soldering iron to get access. As well as this, it gives a nice amount of space for multimeter probes. I also tried to keep the individual logic chips in a similar arrangement as the schematic. This is meant to be used as a learning device, so it’s useful for the chips to line up with the diagram. The header pins for the inputs and outputs are placed on opposite sides of the board to make it more obvious for the user to see it. And the pins have designators written on the board so the user can see what each pin does. The input and output busses are placed in fairly logical places, and grouped together. There is no point having all the A inputs intertwined with the B inputs. The pins for the power and ground are on opposite sides with their own headers, only one needs to be connected for it to work. The LEDs that are directly attached to the pins are placed closer to the logic circuitry, but labeled clearly on the silkscreen. Most of the routing to the LEDs is on the underside of the board, else the top could get confusing. All the designators for components have been made half the normal size due to the small amount of parts used in the project. The below images show the PCB layout I created with the top copper being red, bottom copper being blue, and the silkscreen shown in yellow.

Top Copper

As you might be able to see, I have tried to keep all the power on the bottom side of the board. This leaves lots of space for the logic signals on the top, where the user is more likely to see. As you can see, most of the inputs and outputs of the circuit are also on the bottom side. This is because the way the busses work and input into the adder needs lots of crossing over and would add confusion into the design. This is why labels were used instead.

Bottom Copper

To make it easier to see, I made a larger image of the first and last adder in the series. As you can see, the only real difference in them is that the first has the add/subtract input shown by an LED, whereas the last shows the carry from the previous adder (C0). This is because the A/D bit is attached to all the adders, but the first bit doesn’t have a carry bit input. The carry on that adder is the input for the A/S. It serves the function of inverting the first bit, so that it works like 2’s complement when in subtract mode.

The layout of the first adder in the series
The layout of the last adder in the series

As noted above I used 7400 LVC series logic gates. The SOT23-5 package chips have the suffix of “BVD”. See the datasheets for each of the devices for more information. I have written a simple bill of materials below:

12x SN74LVC1G86DBVT – XOR gate
8x SN74LVC1G08DBVT – AND gate
4x SN74LVC1G32DBVT – OR gate
17x DO-214 LED’s
17x 0805 220Ω resistors
6x 5-pin 0.1″ header pins

The main downside to this type of adder is that is is very slow. Especially when you get to high bit amounts that you are trying to add. This adder will take at least 4 times as long as a single adder to add the two numbers together because the signal has to propage through 4 full adders. This problem is known as propagation delay, each logic chip will take a very short time to compute the output. Although this time is not perceivable by the human eye, if there are 100’s of logic gates in a row, then the delays start to add up and be a problem. If this circuit is to be used in a computer, it could need to make calculations thousands, or maybe millions of times a second, and a carry bit adder is not generally good at that. There are other, faster adders that I will show in a future post.

How a Voltage Regulator Works: LM7805

Voltage regulators are one of the first electronic components you get introduced to as a hobbyist. Really useful when starting out, it simply takes a voltage that is too high, and reduces it down to a set voltage that you want, usually defined by the component. Solves the problem of having batteries or power supplies being a different voltage to the thing you are powering (such as your Arduino), and at as little as 50p from ebay they are easily acquired. Sounds like a great solution, but there is an issue, they are terribly inefficient. They are known to get very hot when used at high currents, and often need hefty heatsinks to stop the magic smoke from being released. To demonstrate why they get so hot we need to think about what happens during use. Remembering Kirchoff, the current going into a system is the same as the current going out of the system. If we use a simplified version of the regulator, the only thing this device changes is the voltage of the output. Due to the minimal current lost powering the circuit we assume the vast majority of power lost is in heat. Using the basic equation of:

Power (W) = Voltage (V) x Current (I)

So if we use an example of the LM7805 made by On Semiconductor (previously Fairchild) that can regulate 5V at 1A. It’s a pretty standard component, and is very typical of a voltage regulator.

If we use a 9V input the power going in is 9V x 1A = 9W.

The output power is 5V x 1A = 5W.

This means that there is 4W of power being dissipated from the regulator as wasted heat. This is a large amount when considering the size of the packages available. When thinking about problems excessive heat can cause in a circuit, it can quite easily damage itself and other components around it when not designed properly. It is why there are often big chunks of aluminium attached to the back of the components to act as a heat sink.

7805
7805 chip in a TO-220 package. Notice the heat sink on the rear with a screw mount.

This post isnt meant to dissuade you from using regulators, they have their place in electronic circuits, and are a great starting point. All electronic engineers need to have a broad understanding of the advantages and disadvantages of linear voltage regulators to be able to handle them properly.

How it Works

LM78xx schematic 2 coloured
Schematic of the silicon inside an LM78xx device, coloured relating to the function of each area.

The above schematic can be found on the datasheet, but it’s been coloured in to show the different sections of the circuit.

The most important component in the above schematic is Q16 (Red), it controls the current between the input and output, therefore the voltage. It is placed in a darlington pair configuration with Q15 (Orange). In this configuration Q16 is amplifying the current amplified by Q15. This means that Q15 can be used to introduce error feedback. The Blue section contains a voltage divider that scales the output voltage so that it can be used by the bandgap circuit. This bandgap circuit is found in the yellow section (Q1 and Q6). This bandgap reference produces an error signal that is fed into Q7 (orange). A bandgap is used because it can provide a stable output even when the temperature of the device changes.

The orange section takes this error and amplifies it through Q15 and the darlington configuration described earlier. The purple section has overheating protection (Q13) and excessive output current protection (Q14). Occasionally on these schematics you also find excessive input voltage protection marked as Q19 in this section. These shutdown the regulator in fault conditions like overcurrent or getting too hot. The Green section is known as the “start up” circuit, because it provides the initial current needed to power the bandgap circuitry. This gives a jumpstart to the circuit when it needs it.

I chose the LM7805 because 5V is a common value to be used, but the LM78xx series has many different preset voltage versions. The bandgap circuit is trying to get its input to 1.25V, this is from the voltage divider found in the blue section. As R20 is a variable resistor, the voltage divider can be calibrated during manufacture to output exactly 1.25V at any chosen output voltage. This is great for a manufacturer because they make lots of the same chip, and it can be made to suit any voltage output they want. This is also similar to the way some adjustable voltage regulators work, such as the LM317. In adjustable chips, the voltage divider is made by the designer externally, meaning it can be applied to any situation with a simple change of resistors.

Basic Configuration

Looking at the datasheet, there are many applications for the device. but the simplest one is just an input and an output. All that’s needed is a couple of decoupling capacitors to smooth out AC signals and random noise. Voltage regulators work best with clean, smooth power. There is also the need, due to the voltage drop across the transistors, for the input voltage to be at least 2V above the required output. This is always a good rule of thumb to go by when it comes to regulators.

LM78xx basic configuration
LM78xx basic configuration

I would recommend people read the datasheet and have a play with different voltage inputs and current outputs, see how easy it is for it to get hot. In that datasheet there are some other good applications using the device, you can turn it into an adjustable voltage output, constant current supply and high current supply. These are also good projects for learning more about transistors and op amps. Equally, there are other types and brands of regulator out there, some cheap, and some quite expensive, it is worth shopping around for  the ones that suit you.