2. Converting Between Binary and Decimal

Learning Objectives Define the binary and decimal number systems. Explain the concept of place value in both binary (base-2) and decimal (base-10). Convert an 8-bit binary number to its decimal equivalent. Convert a decimal number (up to 255) to its binary equivalent. Identify the value of each bit in an 8-bit binary number (1, 2, 4, 8, 16, 32, 64, 128). Explain why computers use the binary system for data representation. How can a computer understand your favorite game, video, and homework using only two numbers, 0 and 1? 🤔 In this lesson, we'll unlock the secret language of computers! You will learn about binary (the computer's language) and decimal (our everyday number system) and master how to translate between them. This is a fundamental skill for understand...

TermDefinitionExample Decimal (Base-10)The number system we use every day. It uses ten unique digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).The number 152 is a decimal number. Binary (Base-2)The number system computers use. It only uses two unique digits: 0 and 1.The number 1011 is a binary number. BitShort for 'Binary Digit'. It is the smallest unit of data in a computer and can be either a 0 (off) or a 1 (on).In the binary number 1011, each digit (1, 0, 1, 1) is a bit. ByteA group of 8 bits. A byte is often used to represent a single character, like the letter 'A'.01000001 is one byte that represents the letter 'A'. Place ValueThe value a digit has based on its position in a number. In decimal, place values are powers of 10 (1s, 10s, 100s). In binary, they are powe...

Binary to Decimal Conversion Sum of (Digit × Place Value) To convert a binary number to decimal, you multiply each binary digit by its corresponding place value (a power of 2) and then add all the results together. Place values start from 2^0 on the right. Decimal to Binary Conversion Repeated Division by 2 To convert a decimal number to binary, you repeatedly divide the decimal number by 2. The remainders from each division, read from bottom to top, form the binary number.