Binary Numbering System

Binary Numbering System

• Named after its base, which is 2
• Has 2 digits: 0 and 1
• Position values for a binary number are 2^x, where x is an exponent, and each position is twice the weight of the preceding one

Importance in Digital Electronics and Computing

• Used extensively in digital electronics and computing due to ease of representation using switches (0 = "off", 1 = "on")
• Allows for electronic storage and manipulation of data using digital circuits

Representation and Manipulation

• Used for representing and manipulating large binary numbers or expressing memory addresses in a compact format
• Computer programs and programming languages use number system concepts to perform arithmetic operations, store data, and communicate with hardware devices

Binary Arithmetic Operations

• Addition
  • 0 + 0 = 0
  • 0 + 1 = 1
  • 1 + 0 = 1
  • 1 + 1 = 10 (write 0, carry 1 to the next higher bit)
• Subtraction
  • 0 - 0 = 0
  • 1 - 0 = 1
  • 1 - 1 = 0
  • 0 - 1 = 1 with borrow from the next higher bit
• Multiplication
  • 0 * 0 = 0
  • 0 * 1 = 0
  • 1 * 0 = 0
  • 1 * 1 = 1
  • Multiply each digit of the second number by each digit of the first, then sum the results
• Division
  • Divide a dividend by a divisor to find a quotient and possibly a remainder
  • Subtract in binary, bringing down the next digit