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**EET 205**

**Digital Electronics**

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**Lab # 3**

**Arithmetic Operations**

**Adders, Two’s Complement**

“I have been asked … ‘If you put into the machine wrong figures, will the right answers come out?’ I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.”

–Charles Babbage

*Objectives:*

To understand the combinatorial logic used in arithmetic functions.

**WARNING! MAKE SURE ALL YOUR INPUTS ARE SET TO +5V OR TTL. USING ANYTHING HIGHER WILL GET YOUR CHIPS VERY UPSET!**

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**WARNING 2! YOU WILL BE USING CMOS INTEGRATED CIRCUITS IN THIS LAB. THESE DEVICES ARE STATIC SENSITIVE – YOU MUST USE A GROUND STRAP WHEN HANDLING THESE COMPONENTS!**

*Exercise 1. Two-bit Adder from Discrete Components*

Build the 2-bit adder with carry that we covered in lecture. Connect the inputs to logic switches and try every combination of inputs A_{1}A_{0 }and B_{1}B_{0}. Do you get the right answers?

**(Remember, A _{1} and B_{1} are the 2s’ place of each number; A_{0} and B_{0} are the 1s’.)**

Here’s a block diagram of the circuit:

*Exercise 2. Two’s Complement Engine*

Build a two’s complement engine. Here’s how you do it: set B_{1}B_{0} = 01. Then use a 7404 inverter to complement the bits of the number A_{1}A_{0} and connect the outputs to the A-input of your adder. Now you are complementing the number and adding 1, which is the prescription for generating the two’s complement. Try several numbers, but first calculate the two’s complement of the input to see if you get it right.

Here’s the block diagram:

*Exercise 3. Subtraction Engine*

Wire up a second 2-bit adder and connect the output of your two’s complement engine to one input and connect two logic switches to the other input. You can now subtract one number from another. Try it with several combinations, but do the arithmetic for yourself first.

Here’s the block diagram. Note that the *carry* is now a *borrow*.

*Exercise 4. 4-bit Full Adder*

Go on the web and find the data sheet for a CD74ACT283E (this may be the hardest part of this exercise – lots of vendors want to sell you one and it’s hard to find just the data sheet). Check out the pinouts then get one from the bins and wire it up.

(You might try calling it a 74LS283, which is logically but not electrically equivalent.)

CAUTION! USE A GROUND STRAP – THESE DEVICES ARE STATIC SENSITIVE!

How many possible combinations of two 4-bit numbers, including carry, are there?

(*Hint: how many input bits are there?*)

Try 10 to 15 of these combinations, with and without carry to see how it works.