How many rows does a truth table need for an expression with n inputs?

It needs 2ⁿ rows, one for every possible combination of input values.

In what order should the input combinations be listed?

They should be listed by counting up in binary from all zeros to all ones, which guarantees that no combination is left out and none is repeated.

Why is it worth adding intermediate columns to a truth table?

Working out each bracketed or negated part in its own column, in precedence order, makes the final output column much less error-prone and shows where a mistake was made.

WJEC A-Level Computer Science 601-5345-3

Hardware: Architecture, Memory and Storage

Topic overview Components of a computer system and how they connect Von Neumann architecture and the CPU The fetch-execute cycle Memory and caching Parallel processing Input and output devices and their uses Secondary storage, fragmentation and defragmentation

Networks and Data Transmission

Topic overview Serial and parallel transmission Simplex, half duplex and full duplex Multiplexing and switching Packets and the TCP/IP protocol stack Networks, standards and protocols Collisions and shared media Routing, addressing and the internet

Logic Gates and Boolean Algebra

Topic overview Logic gates and their truth tables Boolean notation and expressions Building and reading truth tables Boolean identities and rules Simplifying Boolean expressions De Morgan's laws Masking and clearing registers

Data Representation and Data Types

Topic overview Bits, bytes and words The binary number system Hexadecimal notation Character sets and storing characters Primitive data types and storage requirements Binary arithmetic and negative numbers Real numbers, truncation and rounding

Data Structures

Topic overview Data structures and data types One-dimensional arrays Two-dimensional arrays Manipulating arrays Records and fields Arrays of records Choosing a data structure

Organisation of Data: Files and Records

Topic overview Files, records and fields Fixed and variable length records Master and transaction files File access and organisation methods Sequential file access and update algorithms File security, backup and archiving Data validation and verification

Database Systems

Topic overview Flat files and the relational model Relational and other contemporary database systems Primary, foreign, composite and candidate keys Indexes and links between tables Entity relationship modelling Normalisation to third normal form The database management system, queries and user views

The Operating System

Topic overview The need for an operating system The kernel and process management Memory protection and the backing store The user interface between user and hardware Directory structures and file attributes Utility software Batch, real time control and transaction processing

Algorithms and Programs

Topic overview Defining and designing algorithms Variables, constants and identifiers Scope, subprograms and parameter passing Sequence, selection and repetition Mathematical and logical operations Standard algorithms: sorting, searching and compression Dry running, trace tables and test data

Principles of Programming

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Systems Analysis

Topic overview The systems life cycle and the feasibility study Methods of investigation Analysis, abstraction and decomposition Design and data flow diagrams Testing and changeover Maintenance Backup, recovery and documentation

Software Engineering and Program Construction

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Types of Software System

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Practical Programming

Topic overview Designing data structures: fields, records and data types Key fields and methods of access Validation of input data Designing routines with pseudocode Tracing code and test data Prototyping and evaluating a solution Annotated listings and readable code

Data Security and Integrity

Topic overview Dangers of holding files of personal data Levels of permitted access and access control Passwords and authentication Clerical procedures and write-protection Threats to computer systems Malicious and accidental damage to data Contingency planning and disaster recovery

Computing, Society and the Law

Topic overview Social and economic change from computing Computers and the nature of employment The digital divide and cultural change Environmental cost of computing Data protection and freedom of information law The Computer Misuse Act 1990 and computer crime Copyright, surveillance and professional codes

Advanced Data Structures and Logic

Topic overview Arrays in three dimensions Stacks and queues using pointers and arrays Linked lists using pointers and arrays Binary trees using pointers and arrays Hash tables and collision resolution NAND, NOR and Boolean simplification Masking, clearing registers and encryption

Recursion, Sorting and Searching

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Programming Paradigms and Translators

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System Design and Human-Computer Interaction

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Software Engineering Tools and Professional Practice

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Advanced Architecture and Assembly Language

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Communication Networks and File Organisation

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Number Representation and Floating Point

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Databases and Distributed Systems

Topic overview Consistency, redundancy and data independence Relational organisation and normalisation Restructuring data into third normal form Entity relationship modelling Query languages and SQL Validation, verification and the DBMS Big Data, data warehousing and mining Distributed systems and distributed databases

Operating System Management

Topic overview Types of operating system Interrupts and interrupt handling Memory management and partitioning Buffering and data transfer Scheduling and process states Scheduling policies and priorities Evaluating operating system design

Software Systems and Applications

Topic overview The range of software system types Safety related and safety critical systems Computer control and automation The scope of automation in practice Expert systems The internet, intranets and search Selecting and evaluating a software system

Data Security, Cryptography and Attack

Topic overview Integrity problems in online updating The need for cryptography Symmetric and asymmetric techniques Classical ciphers and cryptographic algorithms Comparing cryptographic strength Biometric technologies Malicious software and its vectors Attacks, defence and penetration testing

Logic Gates and Boolean Algebra

Building and reading truth tables

3 things to know
AS Unit 1

Overview

Complete truth table of A·B + ¬A and complete truth table of ¬(A·B).

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

For the expression A·B + ¬A, what is the output when A = 0 and B = 0?

Key term

For the expression A·B + ¬A, what is the output when A = 1 and B = 0?

Key term

For the expression A·B + ¬A, what is the output when A = 1 and B = 1?

Questions from this subtopic

Each one with the model answer underneath.

1
How many rows does a truth table need for an expression with n inputs?
Model answer
It needs 2ⁿ rows, one for every possible combination of input values.
2
How many rows does a truth table for three inputs have?
Model answer
It has 2³ = 8 rows.
3
In what order should the input combinations be listed?
Model answer
They should be listed by counting up in binary from all zeros to all ones, which guarantees that no combination is left out and none is repeated.
4
Why is it worth adding intermediate columns to a truth table?
Model answer
Working out each bracketed or negated part in its own column, in precedence order, makes the final output column much less error-prone and shows where a mistake was made.
5
For the expression A·B + ¬A, what is the output when A = 0 and B = 0?
Model answer
A·B is 0 and ¬A is 1, so the output is 0 + 1 = 1.
6
For the expression A·B + ¬A, what is the output when A = 1 and B = 0?
Model answer
A·B is 0 and ¬A is 0, so the output is 0.

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Hardware: Architecture, Memory and Storage

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Logic Gates and Boolean Algebra

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Fetch, , execute.

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AEncryption is reversible.

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Building and reading truth tables

Overview

What you need to know

For the expression A·B + ¬A, what is the output when A = 0 and B = 0?

For the expression A·B + ¬A, what is the output when A = 1 and B = 0?

For the expression A·B + ¬A, what is the output when A = 1 and B = 1?

Questions from this subtopic

How many rows does a truth table need for an expression with n inputs?

How many rows does a truth table for three inputs have?

In what order should the input combinations be listed?

Why is it worth adding intermediate columns to a truth table?

For the expression A·B + ¬A, what is the output when A = 0 and B = 0?

For the expression A·B + ¬A, what is the output when A = 1 and B = 0?

Other ways to work this

What is inside Levo

The 3-step method, run for you

Cram a whole paper in one sitting

Blank Blitz makes facts automatic

Build It gets the exam shape right

Test It catches misconceptions

Brain Breaks between sessions

Every question in Logic Gates and Boolean Algebra, on a schedule.