Logic Gates
1. Logic gates
On the left is the input to a series of logical circuits.
Indicate the resulting output on the right (1 = on, 0 = off) as well as the intermediate binary values at the exit of each gate:
| Logic Gates | Intermediate value | Output (1 or 0)? |
|---|---|---|
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2. Truth table 2 inputs:
Complete the truth table of the following logic circuit:
3. Truth table 4 inputs:
Complete the truth table of the following logic circuit:
| Input 1 | Input 2 | Input 3 | Input4 | Output |
|---|---|---|---|---|
4. Half adders and Full adders
We have seen the half adder logical circuit in class, but we haven’t actually seen why it’s called a half adder. Consider this, if you are trying to add two numbers in a row such as 1 +1 +1. If you try putting two half adder circuits in a row, you will have a problem! The output of one gate would have a sum and a carry, we need to have three inputs in the following gate to perform the following addition! That’s when the full comes in handy:
Fill out the truth table of the full adder:
| A | B | Cin | S | Cout |
|---|---|---|---|---|
5. Exam easy or hard?
The first section of students of Tech Support collectively decided not to study for their mid-term exam and instead build a truth table to predict if the exam will be easy or hard based on their teacher’s mood.
They built a logic gate diagram, where the output is a light bulb. If it turns on, the exam will be easy, and everyone passes.
They have four switches that can turn on/off independently. The first switch represents if the weather is above 0 degrees Celsius in Canada. The second switch represents if it’s snowing outside (negative temperatures). The third switch represents if the exam is happening on a Thursday and the last switch represents if the exam is happening on a Friday.
- Let’s imagine it is snowing on Exam Day. Build a truth table.
Hint: Observe the inputs and the gates well. You do not need to try all possibilities.
| The temperature is above 0 ° C ? | It is a Thursday? | It is a Friday? | Exam is easy? |
|---|---|---|---|
Let’s imagine it is not snowing on the Exam Day. Build a truth table for all possibilities. | The temperature is above 0 ° C? | It is a Thursday? | It is a Friday? | Exam is easy or not? | | ——————————– | —————– | ————— | ——————– | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
One of the inputs seems to not affect the output, which one is it?
Simplify the logic circuit be removing this gate.
Solution
- Logic gates
| Input | 1 (on) or 0 (off)? |
|---|---|
| 1 0 | 0 |
| 0 1 | 1 |
| 0 1 | 1 |
| 1 0 0 1 | 1 |
Truth table 4 inputs and 1 output:
| Input 1 | Input 2 | Input 3 | Input4 | Output |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 |
| 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 | 0 |
Truth table 2 inputs 1 output:
| Input | Output |
|---|---|
| A: 0 B: 0 | 1 |
| A: 1 B: 0 | 0 |
| A: 0 B: 1 | 1 |
| A: 1 B: 1 | 1 |
Full Adder Truth Table:
| A | B | Cin | S | Cout |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |