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
- Start from the far right (least significant bit) and progress to the left (most significant bit), similar to traditional mathematical addition.
- Apply the binary addition rules as mentioned earlier.
- If a carryover is generated, add it to the next pair of bits on the left.
- 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).