Eletrônica Digital - Sistemas Numéricos

Introduction to Digital Electronics

Overview of the Lesson

• The lesson begins with a warm greeting and an introduction to the objectives, which include reviewing decimal number systems and learning about conversions between different numbering systems.

• The focus will be on three main numbering systems: decimal, binary, and hexadecimal. Other systems may exist but are not covered in this lesson.

Decimal Number System

• The decimal system is explained as having each position represented by a power of 10. For example, in the number 2745:

• 5 times 10^0

• 4 times 10^1 = 40

• 7 times 10^2 = 700

• 2 times 10^3 = 2000

• Counting in the decimal system is linked to human anatomy (ten fingers), leading to digits ranging from 0 to 9 before resetting back to zero.

Binary Number System

• The binary system uses only two digits: zero and one. Each position represents a power of two instead of ten.

• In binary counting:

• Each digit changes based on its position; for instance, the first digit changes every time (every single count), while subsequent digits change at intervals (e.g., every two counts for the second digit).

Conversion Between Systems

• To convert from binary to decimal:

• Each bit is multiplied by its corresponding power of two. For example, for binary 101:

• 1 times 2^2 + 0 times 2^1 + 1 times 2^0 = 4 + 0 + 1 = 5.

• To convert from decimal to binary:

• Divide the number by two repeatedly and record remainders. For example, converting 25 results in 11001 in binary through successive divisions.

Hexadecimal System Introduction

Understanding the Hexadecimal System

Introduction to Hexadecimal

• The hexadecimal system is based on 16, where positions are expressed as powers of 16 (e.g., 16^0, 16^-1).

• In hexadecimal, digits range from 0 to 9 and then use letters A to F for values ten to fifteen.

Conversion Between Number Systems

Hexadecimal to Decimal

• To convert from hexadecimal to decimal, multiply each digit by its corresponding power of 16. For example, in the number 356 (hex), it equals 3 times 16^2 + 5 times 16^1 + 6 times 16^0 = 854 (decimal).

• Another example is converting the hexadecimal number "2F" into decimal: 2 times 16^1 + F(15) times 16^0 = 47.

Decimal to Hexadecimal

• Converting from decimal to hexadecimal involves dividing the number by 16 and recording remainders. For instance, converting "423" gives a result of "1A7" in hex.

Binary Representations

Hexadecimal to Binary

• Each hexadecimal digit corresponds directly to a four-digit binary equivalent. For example, '9' in hex is '1001' in binary.

Binary to Hexadecimal

• To convert binary back into hexadecimal, group binary digits into sets of four and match them with their hex equivalents.

Conclusion and Activity Suggestion

• Viewers are encouraged to find online tools or apps that facilitate conversions between these numeral systems.