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The student should demonstrate knowledge ofsimple binary arithmetic, and the mechanics of its use. Each student is required to design, simulate, build, and test a 2-bit full adder.
By now, you have become familiar with how to do arithmetic with binary numbers. Let's examine how to generate boolean equations (andtherefore how to build a circuit) that describe this process.
To begin with, consider the problem of adding two single bit numbers. This can result in a two-bit answer (1 + 1 = 10). The resulting circuit will therefore need to have two inputs and two outputs. The truth table for this circuit is shown below:
| A | B | C | S |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
C = AB
S = A¢B + AB¢
A device that implements these two functions is known as a half adder. This adder is referred to as ``half'', because it only solves half the general problem of adding numbers with more than one bit. Let's take a look at an example of what happens when we add two (unsigned) 8 bit numbers:
| (Carry) | (0) | (1) | (1) | (1) | (0) | (0) | (0) | |
| A= | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| B= | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
| Cin | A | B | Cout | S |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 |
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S = A¢B¢C + AB¢C¢+ A¢BC¢+ ABC
Cout = AB + AC +BC
We can implement the function for Cout in a straightforward manner, as shown below:
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S = A ÅB ÅC
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You are going to buld a device which will add 2 unsigned 2 bit numbers. Use a pair of switches for each imput value. The results will be displayed on LEDs. You will need to build two copies of the full adder. The carry input to the right most adder will be tied to GND. The carry in of the left adder will be tied to the carry out of the right adder. What happens to the carry out of the left adder?
In block diagram form:
1 - 7486 2 - 7408 2 - 7432
A note about simulation: In this simulation, you will build some simple circuits with gates, then use multiple copies of those circuits to build a larger, more complicated device. This is typical of how system design is done. We use this same kind of procedure with Computer Aided Design (CAD) tools, like your digital simulator. Ideally, you would like to enter the circuit for a full adder once, test and debug it, then turn it into a part we can use over and over again. Then you could simply use two of those parts and draw the connections between them to build your two bit adder. This is called a hierarchichal design. In Digital Works, hierarchy is achieved by using macros. You used a macro in the previous lab for the 7447 driver chip. This week, you will want to create your own macro for the full adder circuit. See the online Digital Works ``Getting Started'' guide for details on how. Once your macro is created, you will create another schematic that uses two copies of the macro, and adds the switches and lights. Your resulting schematic should look like the block diagram of the circuit shown above.
Turn in copies of the schematic for you full-adder macro as well as your final circuit in lab.
HINT: It will probably be easier if you use one 7408 and one 7432 for each carry generator rather than using one chip for parts of both full adders. This way the two carry circuits can have identical pin assignments and also be physically separate to help avoid confusion. This also makes it possible for you to label the pins correctly inside your full adder macro.
