Boolean logic – Technology for Learners

Spotlight on: Logic Circuits

Will Fastiggi — Sun, 07 Aug 2016 19:05:15 +0000

Logic circuits are designed to perform specific functions that enable computers to run properly.

Every logic circuit is made up of several logic gates, which take binary inputs and produce binary outputs. The relationship between these inputs and outputs is based on a certain type of logic, which is represented by boolean algebra.

The most common Boolean operators are AND, OR and NOT.

A NOT gate has only one input. The output of the circuit will be the opposite of the input. If 0 is input, then the output is 1. If 1 is input, then 0 is output.

Truth tables provide all the possible results of a Boolean algebra statement. They are used to check the output from a logic gate or logic circuit. In the example above, if A is the input and Q is the output, the truth table looks like this:

A	Q
1	0
0	1

The NOT gate is the only logic gate with one input; the other five gates have two inputs.

The NOT Boolean expression is written as Q = NOT A.

An AND gate can be used on a gate with two inputs. AND tells us that both inputs have to be 1 in order for the output to be 1.

AND gate truth table:

A	B	Q
0	0	0
0	1	0
1	0	0
1	1	1

The AND Boolean expression is written as Q = A AND B.

The NAND gate behaves in the opposite fashion to the AND gate. You can think of it as an AND gate followed immediately by a NOT gate. Its output is 0 when the two inputs are 1, and for all other cases, its output is 1. The name NAND comes from joining NOT and AND. The symbol for NAND is the same as that for AND except for the addition of a small circle on the right side.

A	B	Q
0	0	1
0	1	1
1	0	1
1	1	0

The NAND Boolean expression is written as Q = A NAND B

The OR gate has two inputs. One or both inputs must be 1 to output 1, otherwise it outputs 0.

OR gate truth table:

A	B	Q
0	0	0
0	1	1
1	0	1
1	1	1

The Boolean expression is written as Q = A OR B.

A NOR gate can be thought of as an OR also followed by a NOT. The output, Q, is 1 if neither input A nor B is 1.

NOR gate truth table:

A	B	Q
0	0	1
0	1	0
1	0	0
1	1	0

The Boolean expression is written as Q = A NOR B

The exclusive OR (XOR) gate works the same as an OR gate, but will output 1 only if one or the other (not both) inputs are 1.

XOR gate truth table:

A	B	Q
0	0	0
0	1	1
1	0	1
1	1	0

The Boolean expression is written as Q = A XOR B.

Complex logic circuits are made up of several logic gates that are built up into chains of logical decisions. The diagram below shows a complex logic circuit combining three simple gates. The first two logic gates are OR gates, the third logic gate is an AND gate.

Altogether there are three inputs (A, B and C), which lead to eight possible outcomes. To solve the truth below, first find D, then E and finally F. Complete a whole columnn before moving on to the next column. D depends on A or B, E depends on B or C, and F depends on D and E.

This logic gate truth table is written as:

A	B	C	D = A OR B	E = B OR C	F = D AND E
0	0	0	0	0	0
0	0	1	0	1	0
0	1	0	1	1	1
0	1	1	1	1	1
1	0	0	1	0	0
1	0	1	1	1	1
1	1	0	1	1	1
1	1	1	1	1	1

Using Scratch to Learn Programming Concepts

Will Fastiggi — Fri, 24 Jul 2015 08:30:22 +0000

Programming is a big part of computer science, and computer science is at the core of our computing curriculum. Since programming is itself at the core of computer science, it’s worth taking some time to really get to grips with both programming as a series of concepts and one of the main tools used in schools to teach these concepts, Scratch.

Programming simply refers to the art of writing instructions (algorithms) to tell a computer what to do. Scratch is a visual programming language that provides an ideal learning environment for doing this. Originally developed by America’s Massachusetts Institute of Technology, Scratch is a simple, visual programming language. Colour coded blocks of code simply snap together in certain ways like a jigsaw, eliminating the typing errors that tend to occur when people use text-based programming languages. Many media rich programs can be made using Scratch, including games, animations and interactive stories. Scratch is almost certainly the most widely used software for teaching programming to Key Stage 2 and Key Stage 3 (learners from 8 to 14 years).

Scratch is a great tool for developing the programming skills of learners, since it allows all manner of different programs to be built. In order to help develop the knowledge and understanding that go with these skills though, it’s important to be familiar with some key programming concepts that underpin the Scratch programming environment and are applicable to any Programming Language. Using screenshots from some of my own Scratch projects, I have written here the main programming concepts that can be learnt through the use of this application.

Sprites

The most important thing in any Scratch program are the sprites. Sprites are the graphical objects or characters that perform a function in your program. The default sprite in Scratch is the cat, which can easily be changed. Sprites by themselves won’t do anything of course, without coding!

Sequences

In order to make a program in any programing language, you need to think through the sequence of steps.

Iteration (looping)

Iteration simply refers to the repetition of a series of instructions. This is accomplished in Scratch using the repeat, repeat until or forever blocks.

Conditional statements

A conditional statement is a set of rules performed if a certain condition is met. In Scratch, the if and if-else blocks check for a condition.

Variables

A variable stores specific information. The most common variables in computer games for example, are score and timer.

Lists (arrays)

A list is a tool that can be used to store multiple pieces of information at once.

Event Handling

When key pressed and when sprite clicked are examples of event handling. These blocks allow the sprite to respond to events triggered by the user or other parts of the program.

Threads

A thread just refers to the flow of a particular sequence of code within a program. A thread cannot run on its own, but runs within a program. When two threads launch at the same time it is called parallel execution.

Coordination & Synchronisation

The broadcast and when I receive blocks can coordinate the actions of multiple sprites. They work by getting sprites to cooperate by exchanging messages with one anoher. A common example is when one sprite touches another sprite, which then broadcasts a new level.

Keyboard input

This is a way of interacting with the user. The ask and wait prompts users to type. The answer block stores the keyboard input.

Boolean logic

Boolean logic is a form of algebra in which all values are reduced to either true or false. The and, or, not statements are examples of boolean logic.

User interface design

Interactive user interfaces can be designed in Scratch using clickable sprites to create buttons.

Concluding thoughts…

By incorporating these key programming concepts, Scratch makes computer science accessible to all learners. In doing so, it promotes problem solving skills, which are important in all areas of life, not just programming. The advantage of using Scratch 2.0 to do this is that it moves the Scratch programming language to the web, making it easier than ever to learn about, share and remix programs.