Adding Binary Numbers

Adding Binary Numbers

Fundamental Concepts

  • A binary number is composed of only two digits, 0 and 1.
  • Binary number addition is similar to the familiar base-10 system addition (decimal), but carried out in base-2.
  • The ‘carry’ operation in binary addition is identical to that in decimal addition.

Binary Addition Rules

  • Adding 0 to 0 results in 0 (0 + 0 = 0).
  • Adding 0 to 1 or 1 to 0 results in 1 (0 + 1 = 1 or 1 + 0 = 1).
  • Adding 1 to 1 results in 0 and carries over a 1 to the next higher bit (1 + 1 = 0, carry 1).

Steps for Binary Addition

  1. Start from the far right (least significant bit) and progress to the left (most significant bit), similar to traditional mathematical addition.
  2. Apply the binary addition rules as mentioned earlier.
  3. If a carryover is generated, add it to the next pair of bits on the left.
  4. Remember, a carryover occurs when two bits of 1 are added together.

Handling Overflow in Binary Addition

  • In computing, overflow occurs when a calculation results in a number too large for the given storage capacity, for instance when adding two large binary numbers.
  • If a carry is obtained from the addition of the most significant bits, it represents an overflow.
  • An understanding of binary addition is crucial in diagnosing and tackling overflow errors.

Example of Binary Addition

  • Consider two binary numbers, 1101 and 1011.
  • From right to left, the addition would proceed as follows: 1 (carry) 1101 + 1011 ____ 11000
  • Here, binary 1101 (13 in decimal) plus binary 1011 (11 in decimal) equals binary 11000 (24 in decimal).