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  A decimal number, also known as a base-10 number, is the most common numerical system used in everyday life. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The decimal system is positional, meaning the value of a digit depends on its position within the number. Each position is a power of 10.  ### Positional Notation In a decimal number, each digit is multiplied by a power of 10 based on its position from the right (starting at 0). For example, in the number 3456: - The digit 6 is in the 10^0 place (units) - The digit 5 is in the 10^1 place (tens) - The digit 4 is in the 10^2 place (hundreds) - The digit 3 is in the 10^3 place (thousands) So, the value of 3456 is calculated as: \[ 3 \times 10^3 + 4 \times 10^2 + 5 \times 10^1 + 6 \times 10^0 \] \[ = 3000 + 400 + 50 + 6 \] \[ = 3456 \] ### Converting Between Decimal and Other Bases #### Binary (Base-2) to Decimal Computers use binary (base-2) because they operate on two states: on and off. A binary number uses only the...

  Binary numbers are a fundamental part of digital systems and computer technology. Understanding binary numbers involves grasping the base-2 numeral system, which is the foundation of binary arithmetic and digital circuit design. Here's a comprehensive explanation: 1. Definition and Basics Binary Number System : The binary system is a base-2 numeral system. It uses only two digits: 0 and 1. Each digit in a binary number is called a bit, which stands for binary digit. 2. Binary vs. Decimal Systems Decimal System : The standard numeral system used in everyday life is the decimal system, which is base-10 and uses digits from 0 to 9. Binary Representation : Each binary digit (bit) represents an increasing power of 2, starting from the rightmost bit, which is the least significant bit (LSB). 3. Binary to Decimal Conversion To convert a binary number to a decimal number, sum the products of each bit and its corresponding power of 2. For example, the binary number 1011 can be converted ...