Lesson Plan

# Boolean Logic

Introduction Lesson to Boolean Logic using Minecraft
Niamh G.
Director of Instructional Technology
NYC DOE Affinity Field Support Center
My Grades 6, 7, 8, 9, 10, 11, 12
My Subjects English Language Arts, Math, Science, Social Studies, Arts, World Languages, English Language Learning, Health & Wellness
Objectives

Students will be able to...

• explain the basis of logic
• link logic to George Boole’s theories and computer programming
• operate and use a simple truth table in the application of logic to solve the puzzle

Subjects
Math
Science

#### 1 What is Logic?

Activity: Presenting

The term "logic" came from the Greek word logos, which can be translated as "opinion", "expectation", "reason", or "argument". Hence logical reasoning is a process in which statements are collected together in an argument, with the intention of providing support or evidence for some conclusion. Logic as a science is concerned with the evaluation of arguments, namely with deciding whether they are correct or not, as well as being consistent, complete and sound.

For example, consider the following –

Mary is human,
Humans are mortal (Assumptions)

Therefore Mary is mortal. Conclusion.

This is obviously a correct argument in the sense that the conclusion follows from the assumptions. If the assumptions of the argument are true, the conclusion of the argument must also be true.

#### 2 What is Boolean Logic?

Activity: Exploring

Boolean logic categorizes assumptions, treating them as propositions which are either TRUE or FALSE. These statements cannot be anything in between (this is called the law of the excluded middle). Such statements are called Propositions.

o In Boolean Logic, each individual proposition is given a short name. Propositions are labeled, usually with letters like P, Q etc. so that they can be quickly identified.

o Truth values assign meaning to statements and symbols, which can be quickly understood because they are always the same: 1 = TRUE and 0 = FALSE.

o Simple propositions can be connected together using AND, OR and NOT, to form more complex arguments.

o We can use propositions to make equations like in algebra. These are called Boolean equations. For example, for two propositions P and Q, the equation

P=Q
means that proposition P is TRUE whenever Q is TRUE, and P is FALSE whenever Q is FALSE.

Amazingly, these three little symbols can help us produce even the most amazingly complicated arguments or computer programmes, and to check their validity.

Student Instructions

Practice Exercise: Decide which of the following is a proposition and which is not:

(1) What time is it?
(2) John’s T-shirt is red.
(3) This statement you’re reading just now is false.

Solution:

o Only (2) is a proposition, since at any moment in time, it can be either TRUE or FALSE.

o A question is neither TRUE nor FALSE.

o (3) leads to a contradiction: If we assume (3) to be TRUE, then by its own admission, it must be FALSE. If we assume it to be FALSE, then its opposite must be TRUE, which means that the statement must be TRUE. Such a contradictory statement is called a Paradox. In this case the contradiction was caused by the statement making a judgement call about itself. Such statements are said to be “self-referential” and they often lead to paradoxes.

#### 3 Boolean Logic and Minecraft

Minecraft is a construction game that makes heavy use of Boolean logic in both the game play and behind the scenes in the inner workings of the game itself. The game has many modes... such as the creative mode which allows you to build for hours, if that’s what you’re into ... or the survival mode, which can include designing and constructing a fortress to keep you safe from cuboid zombies (Not for the faint hearted!).

The game is known for its stand-out graphics... it is characterized by squares and jagged edges. There are lots of materials available to build with, but the most interesting is probably the Redstone block. Redstone can transmit Power, which is a lot like electricity: it can travel through circuits and activate devices, like say a lamp or an elevator.

#### 4 Minecraft Circuits

Here is a simple circuit: The lever is the INPUT; if you right-click on the lever to switch it ON, you generate current through the Redstone wire, making it glow red. This is the OUTPUT. It can activate a device – in this case a piston.

INPUTS and OUTPUTS can only be in one of two forms: ON or OFF.

 State Symbols used for the state in Boolean logic: ON 1 TRUE T OFF 0 FALSE F

#### 5 Logic Gates

A Logic Gate is a simple circuit which receives one or more INPUTS in the form TRUE/FALSE and gives a desired OUTPUT in the form TRUE/FALSE. A computer is collection of millions of logic gates connected together. If you want to make a computer, you have to know how to make logic gates.

Here is a simple logic gate made of some Redstone wire and a Torch. As a rule, torches always generate current as OUTPUT, except when current flows into them as INPUT :

 INPUT: current into torch OUTPUT: current from torch TRUE FALSE FALSE TRUE

Solution to student work:

 Lever 1 input Lever 2 input Output TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE FALSE FALSE
Student Instructions

Using Minecraft build the following and fill in the corresponding table:

Here is a gate which receives two inputs. It is enough for lever 1 OR lever 2 to be ON, and current will flow. Hence this is called the OR gate. We describe it by a truth table :

 Lever 1 input Lever 2 input Output TRUE TRUE TRUE FALSE TRUE FALSE TRUE FALSE FALSE

#### 6 Wrap-Up

Activity: Conversing

Using insights from Boolean algebra, it can be shown that any type of logic gate in Minecraft can be constructed simply by putting together several NOT gates and OR gates. Similarly, today’s engineers use Boolean Algebra to make electronic circuits suited to ever more complicated tasks.