4 Bit Binary Calculator

If you need to quickly add numbers from 0 to 15, and you know how to rapidly convert to binary and back to decimal, this is for you...But if your human then this is just a fun project!!  I'm going to show you how to make a 4 bit (0-15) adding calculator using 74xx series IC chips.

The chips that I used are the very basic gates like OR, AND, XOR, NOR, NAND, etc.  No actual adding chips are used so its one level up from transistors, and it's totally TLL!**

By the way, this is another addition to the unofficial "Macroelectronics" catagory for all of you who have seen my diy ram instructables!

**If you use the 74hc series or 74hct series, then its technically not TLL, but who cares about the techincal details!!

This project only requires a few parts:

1 Breadboard, maybe 2 - It should have atleast 50-60 rows
2 74xx AND chips - I used the 74hc08
2 74xx XOR chips - I used the 74hc86
1 74xx OR chip - I used the 74hc32
1-2 DIP Switches - I used 2 8 switch DIP switches (I'm gonna expand to 8 bits)
8 1K ohm -or greater- resistors
Lots of wire - Don't yell at me but I use bare copper! Its a bad habit, (some may argue that it's a dangerous one) I know, but I don't care!
 

The basic adding circuit is just that, basic!  It consists of a XOR gate and an AND gate to give you the basic output with a carry bit.

The XOR gate is short for exclusive or.  In a regular OR gate, 0 and 0 equal 0, 1 and 0 equal 1, 1 and 1 equal 1.  In an exclusive or gate, 0 and 0 equal 0, 1 and 0 equal 1, 1 and 1 equal 0.  This is important because when adding 1 and 1 in binary you get 10, so the ones place has a zero, something that can't be done with a basic OR gate.

OR:
A  B  Y
0  0  0
1  0  1
0  1  1
1  1  1

XOR:
A  B  Y
0  0  0
1  0  1
0  1  1
1  1  0

So now, when you add 1 and 0, you get 1, but hold on...When you add 1 and 1, you get 0?? That can't be right! In order to fix that, we need to be able to have 1 and 1 equal 10. Welcome to the AND gate.  As the name implies, an AND gate equals 1 when A=1 AND B=1.  This it tied in parallel with the XOR gate and is the carryout bit, so that when you add 1+1, you CAN get 10!

Ok, so we can add 1 and 1, but what if we want to add 11 and 11, well the problem is that there is no carryin bit on the second adder. We need a full adder. In order to make a full adder, we have to use 2 XOR gates, 2 AND gates and an OR gate. The circuit for the full adder is shown below:

The full adder works by putting inputs A and B through a XOR gate, then taking the output from that and XORing it with the Carry-in.  This gives you the bit output.  To make the Carry-out, you have to put A and B through an AND gate, and put the output of the A XOR B gate and the Carry-in through an AND gate as well. When you put those 2 outputs into an OR gate, you get a Carry-Out bit. So now we can put a bunch of these together and get a calculator.

Now that we have full adders, its time to put them together to make a calculator.  To connect all of the adders together, you have to connect the carry-outs to the carry-ins in a cascading fashion.  So the carry-out of the first adder connects to the carry-in of the second adder and so on.

Below shows the concept.  The blocks represent the adders and the arrows are the carry-ins and carry-outs.

Ther are a few tricks to building this on a breadboard.  The organization of the chips on the board is very important, I found that putting the chips in this order works well: XOR, AND, OR, AND, XOR, then the DIP switches.

Another good idea is to build each adder one at a time and on one side of the logic gates.  There are 2 XOR and 2 AND gates on each side of the chips so that makes construction a lot easier.  The order that I put the wires on were: connections to the DIP switches, inter-gate connections, and finally connections to the LEDs.

To wire up the switches, you first (this may only apply to cmos versions of the chips, I haven't been able to experiment TTL versions yet) connect the side not connected to the adder inputs to the supply voltage.  Next connect the other side (the pins connected to the adder inputs) to ground through a 1K ohm, or greater, resistor.

The LED's are connected to the outputs of the adders through a 1K ohm resistor.  If you are using the 74LS series or similar (any series that can't source 5 mA or more) you will have to connect the output to a transistor to get to the required current.

If you understand the phrase "There are 10 kinds of people in the world, those who understand binary and those who don't" go on to the next step! If not, stay here!

The number system we know and love is base 10. This means that each new column of numbers is 10x the last column (if you don't believe me, divide 10 by 10 and you get 1 or divide 100 by 10 and you get 10, these relate to the 100's, 10's, and 1's columns).  Binary, or base 2, is different in that each column is a power of 2 (so each new column is 2x the last) and it uses only 1s and 0s.

Let's look at binary numbers.  Take the number 10 for example. In binary, 10 is 2 in base 10 because the  first column is the 1's column and the second is the 2's column (1*2=2). If we break this number down, we get 1 in the 2's place and 0 in the 1's. 2+0=2, so 10 is 2. Another number example could be 101.  Now we have 3 columns to work with.  In binary this is the 4's column because 1*2=2, in the 2nd column, and 2*2=4 in the 3rd column.  Let's break this down, there is a 4 and a 1 and no 2s.  4+1=5 so 101=5.

Now that you get the basics of binary, we can learn to convert to binary from base 10.  To convert to binary, you have to subtract the power of 2 that it is greater than the number until you reach 0. This may sound confusing, as it is hard to explain without examples, so thats what we are going to do.  Let's take the number 15.  15 is greater than 8 (powers of 2 include 1, 2, 4, 8, 16, 32, etc.) so we do 8-15=7. We also put a 1 in the 8's column. The next power of 2 is 4. 7-4=3, so we put a 1 in the 4's column. Next is 2. 3-2=1, so we put a 1 in the 2's column. And finally 1-1=0, so we put a 1 in the 1's column.  When we put all of these together we get 1111.

Now let's lake the number 11.  11-8=3, so we put a 1 in the 8's column. 3 isn't bigger than 4, so we have to put a 0 in the 4's column. 3-2=1, so we put a 1 in the 2's coulmn. And finally, 1-1=0, so we again put a 1 in the 1's column. This gives us the binary number, 1011.

Now you have a 4 bit adding calculator, congrats!

I know that there are adding chips in the 74 logic family, and that there is a calculator much more sophistocated in my kitchen drawer, but this fun little project helped me, and hopefully you too, learn more about adding numbers with electronics and logic.

I hope to build an 8 bit adder, as a 4 bit adder is wimpy with up to 15+15, along with subtraction too!