Number Systems

This section covers various number systems, including decimal, binary, octal, and hexadecimal, essential for understanding data representation in digital electronics.

Analogue Versus Digital

This section distinguishes between analogue and digital representations of data, explaining their characteristics and how they relate to physical quantities.

Introduction To Number Systems

This section introduces the fundamental concepts of number systems, highlighting the characteristics and significance of various systems in digital electronics.

Decimal Number System

The decimal number system, a radix-10 system, uses ten specific digits to represent numbers, crucial for understanding numerical representation in digital electronics.

Binary Number System

The binary number system is essential for digital electronics, using only two digits, 0 and 1, to represent all forms of data.

Advantages

The binary number system provides significant advantages for digital computers, including ease of representation, operation efficiency, and compatibility with electronic devices.

Octal Number System

The octal number system is a base-8 numbering system, using the digits 0-7 to represent values and plays a vital role in computing.

Hexadecimal Number System

The hexadecimal number system is a base-16 system that simplifies binary representation and is essential for digital computing.

Number Systems – Some Common Terms

This section covers essential terms related to various number systems such as binary, decimal, octal, and hexadecimal, focusing on their unique characteristics and operations.

Binary Number System

The binary number system is a radix-2 system with the digits 0 and 1, playing a crucial role in digital electronics and computing.

Decimal Number System

The decimal number system is a radix-10 system that utilizes ten digits (0-9) to represent numerical values.

Octal Number System

The octal number system is a base-8 numeral system using digits from 0 to 7, providing an alternative way to represent binary numbers.

Hexadecimal Number System

The hexadecimal number system is a base-16 numeral system that simplifies the representation of binary numbers.

Number Representation In Binary

This section discusses different methods of representing both positive and negative decimal numbers in binary format, including sign-bit magnitude, 1's complement, and 2's complement methods.

Sign-Bit Magnitude

The Sign-Bit Magnitude representation method encodes decimal numbers in binary form where the most significant bit indicates the sign of the number, while the remaining bits express its magnitude.

1’s Complement

The 1's complement representation allows for the encoding of negative numbers in binary by inverting all bits of their positive counterparts.

2’s Complement

The 2's complement method represents signed integers in binary, allowing for straightforward operations like addition and subtraction.

Finding The Decimal Equivalent

This section explains how to find the decimal equivalent of numbers in various number systems, specifically addressing binary, octal, and hexadecimal systems.

Binary-To-Decimal Conversion

This section explains how to convert binary numbers into decimal form, detailing the steps for both integer and fractional parts.

Octal-To-Decimal Conversion

This section focuses on the process of converting octal numbers to their decimal equivalents through the use of place values.

Hexadecimal-To-Decimal Conversion

This section introduces the process of converting hexadecimal numbers to their decimal equivalents, illustrating the methodology through examples.

Decimal-To-Binary Conversion

This section explains the method for converting decimal numbers to their binary equivalents by handling integer and fractional parts separately.

Decimal-To-Octal Conversion

This section outlines the method for converting decimal numbers to octal numbers, emphasizing the process for both integer and fractional parts.

Decimal-To-Hexadecimal Conversion

This section covers the process of converting decimal numbers to hexadecimal representation.

Binary–octal And Octal–binary Conversions

This section covers the processes for converting between binary and octal number systems, emphasizing their base relationships.

Hex–binary And Binary–hex Conversions

This section explores the methods for converting hexadecimal numbers to binary and vice versa, emphasizing the importance of understanding the binary equivalents of hexadecimal digits.

Hex–octal And Octal–hex Conversions

This section explains the methods for converting numbers between hexadecimal and octal systems, primarily using binary as an intermediary step.

The Four Axioms

The Four Axioms summarize the principles of converting numbers between different number systems, focusing on key conversion methods and procedures.

Floating-Point Numbers

Floating-point notation efficiently represents a wide range of large and small numbers while making arithmetic operations easier.

Range Of Numbers And Precision

This section discusses how the range of numbers and precision in floating-point representation is determined by the number of bits allocated to the exponent and mantissa.

Floating-Point Number Formats

Floating-point format allows for the representation of a wide range of values, accommodating both very small and very large numbers in a compact form.

Digital Electronics

This section explores various number systems fundamental to digital electronics, including decimal, binary, octal, and hexadecimal formats.