1. Introduction to Binary Numbers

Learning Objectives Define the term 'binary' and explain why computers use it. Identify a 'bit' as the smallest unit of data and a 'byte' as a group of 8 bits. Explain the concept of a Base-2 number system compared to our Base-10 (decimal) system. Count from 0 to 10 in binary. Convert any 4-bit binary number into its decimal equivalent. Convert any decimal number from 0 to 15 into its 4-bit binary equivalent. Ever wonder how your computer understands everything from your favorite game to your homework? 🎮 It all starts with just two numbers! In this lesson, we'll pull back the curtain and learn the secret language of computers: binary! You'll discover how simple 'on' and 'off' signals can represent every piece of i...

TermDefinitionExample BinaryA number system that uses only two digits, 0 and 1. It is the fundamental language of computers because it represents the 'off' and 'on' states of an electrical switch.The number `1010` is a binary number. BitShort for 'Binary Digit', it is the smallest unit of data in a computer. A bit can have a value of either 0 or 1.In the binary number `1010`, the first `1` is one bit. ByteA group of 8 bits. A byte is a common unit of measurement for digital information and is often used to represent a single character, like the letter 'A'.The byte `01000001` represents the capital letter 'A'. Base-2Another name for the binary system. It's called Base-2 because it only has two digits (0 and 1) to build all its numbers....

Binary Place Value ... 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 Each position in a binary number represents a power of 2, starting from 2⁰ (which is 1) on the far right. Each place to the left is the next power of 2 (2¹, 2², 2³, etc.). Algorithm: Binary to Decimal Conversion Sum of (digit × place_value) for all digits. To convert a binary number to decimal, multiply each binary digit (0 or 1) by its corresponding place value and then add all the results together. Algorithm: Decimal to Binary Conversion Find the largest power of 2 that fits into the number, place a '1' in that position, subtract it, and repeat with the remainder. Start with your decimal number. Find the largest place value that is less than or equal to your number. Put a '1' in that posi...