Binary Arithmetic:-

Introduction:-

Welcome to the world of Digital Logic! Whether you’re a beginner just diving into computer science or an enthusiast eager to strengthen your foundation, this post will introduce you to the world of digital systems.Binary arithmetic operates on the base-2 numeral system, using only two digits: 0 and 1. It involves addition, subtraction, multiplication, and division, similar to decimal arithmetic but follows unique rules. Key concepts include carrying in addition and borrowing in subtraction, essential for digital computing and data representation.Get ready to embark on a journey that will build the base for mastering more advanced topics!

How do we perform binary addition, subtraction,multiplication & division in digital systems?

Here’s a brief overview of how binary operations are performed in digital systems:-

1. Binary Addition:-

• Basic Rules:-
  • 0 + 0 = 0
  • 0 + 1 = 1
  • 1 + 0 = 1
  • 1 + 1 = 0 (carry 1)
  • 1 + 1 + 1 = 1 (carry 1)
• Process:- Align numbers, add from right to left, carry over as needed.

2. Binary Subtraction:-

• Basic Rules:-
  • 0 – 0 = 0
  • 1 – 0 = 1
  • 1 – 1 = 0
  • 0 – 1 = 1 (borrow 1 from the next higher bit)
• Process:- Start from the rightmost bit, borrow if needed, similar to decimal subtraction.

3. Binary Multiplication:-

• Process:-
  • Use a method similar to decimal multiplication:
    • Multiply each bit of the multiplicand by each bit of the multiplier.
    • Shift left for each new bit of the multiplier.
    • Add the results together.
• Example:-
  • To multiply 101 (5) by 11 (3):-
  • 101
    x 11
  • ———
    101 (this is 101 x 1)
    101 (this is 101 x 1, shifted left)
    ———-
    1111 (this is 15 in decimal)

4.Binary Division:-

• Process:-
  • Similar to long division in decimal:-
    • Divide the dividend by the divisor, bit by bit.
    • Subtract and bring down the next bit.
    • Continue until all bits are processed.
• Example:-
  • To divide 1101 (13) by 11 (3):-
    • 11 goes into 110 (3) three times, remainder is 0; bring down the next bit.
    • 11 goes into 01 (1) zero times; final quotient is 11 (3) & remainder is 0.

These operations are fundamental for digital circuits, which use logic gates to implement these arithmetic functions efficiently.