Micro Controller : Logical Components
Logic gates can be configured in such a way that they perform meaningful logical or mathematical operation.
Adding binary numbers.
An XOR and an AND gate can be configured to compute a sum of two binary numbers. As a refresher, here are the first ten values in decimal and binary.
| decimal | binary |
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
Half-Adder.
Adding two binary numbers by hand will yield:
| A | B | carry | sum | decimal | |
| 0 | + | 0 | - | 0 | 0 |
| 0 | + | 1 | - | 1 | 1 |
| 1 | + | 0 | - | 1 | 1 |
| 1 | + | 1 | 1 | 0 | 2 |
Ignoring the carry-over number, the Truth Table for Exclusive OR emerges:
| A | B | A ⊕ B |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Only focusing on the carry-over number, the Truth Table for AND emerges:
| A | B | A ⋀ B |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
The complete Truth Table for adding two numbers becomes:
| A | B | A ⊕ B | A ⋀ B | A + B |
| 0 | 0 | 0 | 0 | 00 |
| 0 | 1 | 0 | 1 | 01 |
| 1 | 0 | 0 | 1 | 01 |
| 1 | 1 | 1 | 0 | 10 |
This can be expressed in with the following circuit.
Click the buttons next to the A and B labels to represent 1 (one) or 0 (zero). Black represents 0 (zero) and orange represents 1 (one).
Full-Adder
While the Half-Adder accepts two values: A and B and returns two values: Sum and Carry. A Full-Adder accepts A and B as before but also the Carry from a previous calculation. This circuit is a some what more complicated but still simple enough for you to follow the orange anf black lines.
Chaining Adders
Half-Adder and any number of Full-Adders can be chained together to compute a larger value.
This interactive allows for adding of two 4-bit numbers. The result is stored in a 4-bit number as well. Toggle the blue circles to indicate 1 or 0 values. Pay special attention to the carry-bit that goes from one adder to the other from right to left when applicable.
Multiplexer.
Ayx + Byx + Cyx + Dyx