Exercise 6.3: ALU Basics

So far we have learned how to represent signed numbers in binary using 2's complement, and we have built a circuit that generates the 2's complement of an input for us.
Now in this section, we will figure out how to perform subtraction using the previously learned circuits, then how to choose between addition and subtraction, and finally understand the basics of an ALU.
With this, we will reach our goal of building our own signed calculator.

1) Binary Subtraction Using 2's Complement

In the previous section on signed arithmetic and overflow, we learned that when we add the 2's complement of a number to itself, we get a 0 in fixed-bit binary arithmetic as a consequence of overflow.
Now that we have a solid representation for negative numbers, let's try subtraction using the same adder circuit we built in the accumulator exercise.

The 2's complement generator's output will be connected to one input of the adder circuit.
The other input of the adder receives the original number, and the output of the adder is stored in the register as before.
Together, the original input, the 2's-complemented input, and the adder form a complete binary subtractor.

Components you'll need:

• 1 × 74LS283 4-bit Full Adder IC
• Previously built 2’s complement generator circuit
• 2 × 4-position DIP switches (one for input A, one for input B)
• 8 × 10 kΩ resistors (pull-down resistors for DIP switches)
• 4 × LEDs (for displaying the result)
• 4 × 220 Ω resistors (current limiting for LEDs)
• Assorted jumper wires
• Breadboard and 5 V power supply

Step-by-step design:

1. With power OFF, place the 74LS283 adder IC on the breadboard so it straddles the center gap.

2. Power the adder:
   * Connect its VCC pin to the 5 V rail.
   * Connect its GND pin to the ground rail.

3. Set up the DIP switch for input A:
   * Connect one side of each of the four switches to 5 V.
   * From the other side of each switch, connect a 10 kΩ resistor to GND.
   * These four lines form bits A0–A3.

4. Connect the four input-A lines directly to the corresponding A inputs of the adder.

5. Set up the second DIP switch for input B in the same way:
   * One side of each switch to 5 V.
   * The other side pulled down to GND through 10 kΩ resistors.

6. Connect these four lines to the four inputs of the 2’s-complement generator circuit.

7. Connect the four outputs of the 2’s-complement generator to the B inputs of the adder.

8. Connect the four sum outputs (S0–S3) of the adder to four LEDs:
   * Each LED must be in series with a 220 Ω resistor.
   * Connect the resistor-LED chain to GND so that a HIGH output lights the LED.

9. Carefully check that:
   * Input A goes straight to the adder.
   * Input B only reaches the adder after passing through the 2’s-complement circuit.
   * All pull-down resistors are connected.
   * Power and ground rails are correct.

10. Turn the supply ON and test:
    * Choose values for A and B using the DIP switches.
    * Verify that the LED pattern corresponds to A − B.
    * Try multiple combinations to confirm correct subtraction.

How does the adder perform subtraction using 2's complement?

-- By disabling the carry output By adding the original number to the inverted version plus one By reversing the bit order By increasing the clock speed

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2) Introducing the Arithmetic Logic Unit (ALU)

In real processors, arithmetic operations such as addition and subtraction—and logical operations such as AND or OR—are grouped into a single block called the Arithmetic Logic Unit, or ALU.
Instead of building separate circuits for every operation, the ALU reuses hardware and selects the desired function using control signals.

In this section, we will study the ALU at a block-diagram level before implementing a simple version ourselves.

The ALU typically has two data inputs, a result output, and a set of control lines that decide which operation is performed.
These control lines are what allow the same internal circuitry to compute sums, differences, or logical results.

3) Selecting Operations Using a Multiplexer

To allow our circuit to either add or subtract, we need a way to choose between feeding the original input bits or their 2’s complement into the adder.
This selection is done using a multiplexer (MUX)—a digital switch that chooses one of several inputs based on a control signal, a concept first explored in Exercise 4.3: Multiplexing.

In this section, we will:

• Insert a MUX before the adder input
• Add a control switch labelled ADD/SUB
• Observe how the same hardware performs two different operations

When the control line selects the direct input, the circuit performs addition.
When it selects the 2's-complemented input, the same adder automatically performs subtraction.

Components you'll need:

Step-by-step design:

1.

What we built so far is the arithmetic part of a simple ALU, which is sufficient to make our own signed calculator. If we add logic gates to this and place in more multiplexers, we get a full fledged Arithmetic and Logic Unit.

Final Submission

Upload a short video (20 seconds) showing your add/subtract circuit working. Demonstrate both operations clearly using different input values on the switches.

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In the next section,, we will try to understand the working of an ALU IC - 74181.