reveal.js

## Constructing an Adder and an ALU

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CS 130 // 2024-10-03

# One-bit Adder

#### Full Adder: Circuit that adds three bits

<table>
    <tbody>
    <tr> <th>A</th> <th>B</th> <th>C</th><th bgcolor="lightgray"></th><th>Y1</th> <th>Y0</th></tr>
    <tr> <td>0</td> <td>0</td> <td>0</td><td bgcolor="lightgray"></td><td>0</td> <td>0</td></tr>
    <tr> <td>0</td> <td>0</td> <td>1</td><td bgcolor="lightgray"></td><td>0</td> <td>1</td></tr>
    <tr> <td>0</td> <td>1</td> <td>0</td><td bgcolor="lightgray"></td><td>0</td> <td>1</td></tr>
    <tr> <td>0</td> <td>1</td> <td>1</td><td bgcolor="lightgray"></td><td>1</td> <td>0</td></tr>
    <tr> <td>1</td> <td>0</td> <td>0</td><td bgcolor="lightgray"></td><td>0</td> <td>1</td></tr>
    <tr> <td>1</td> <td>0</td> <td>1</td><td bgcolor="lightgray"></td><td>1</td> <td>0</td></tr>
    <tr> <td>1</td> <td>1</td> <td>0</td><td bgcolor="lightgray"></td><td>1</td> <td>0</td></tr>
    <tr> <td>1</td> <td>1</td> <td>1</td><td bgcolor="lightgray"></td><td>1</td> <td>1</td></tr>
    </tbody>
</table>
    
</div>
<div>
    
![Full Adder](../../assets/images/combinational_FA.png)
    
</div>
</div>

# Four-bit Adder

## Demo: constructing a 4-bit adder from 1-bit full adders

![4 Bit Adder](../../assets/images/adder4bits.png)

[Adder test vector](../../assets/adder4bit_test_vector.txt)

# ALU

## The ALU
- What does ALU stand for?
    + Arithmetic Logic Unit
- 
 What does an ALU do?
    + Does all the logical and arithmetic operations of the CPU

## Basic ALU
- The simplest ALU conceivable is one that only operates on two 1-bit inputs and can perform only two operations: **AND** and **OR**
    ```py
    def basic_alu(a, b, op):
        if op == "0":
            return (a and b)
        else:
            return (a or b)
    ```
- 
 Let's implement this in Logisim!

### Exercise: Enhance the Basic ALU
1. make it work on 4-bit values
2. add operations for XOR and NOT
 - you will need a bigger multiplexor
 - NOT only works on **A** - ignore **B**
3. Can you include your 4-bit adder?

# Subtraction

## Subtraction

- You can use the same adder circuitry to support subtraction
- convert **B** into it's negative value
 - flip all the bits (NOT gate)
 - add 1 (give a 1 to **Cin**)

[Adder/Subtractor test vector](../../assets/addersubtractor4bit_test_vector.txt)

## Supporting `slt`

You can even use your adder for *set on less than* 
- set the adder to do subtraction  
- look at the highest bit of the result
 + if it is 1, then the subtraction result was negative, so set result to 1
 + if it is 0, then the subtraction result was not negative, so set result to 1