Binary Addition | Computer for GCSE/IGCSE - Year 11 PDF Download

Binary Addition 

• Adding binary numbers is akin to adding denary numbers.

Binary Adding Rules 

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 1 = 10 (Carry 1 to the next left column)
• 1 + 1 + 1 = 11 (Carry 1 to the next left column)

Adding Binary Numbers: Step-by-Step Guide

• Step 1: Start by aligning the two binary numbers you intend to add, placing the least significant bit (LSB) on the right side.
• Step 2: Commence by summing up the LSBs. If the total is 1 or less, jot it down in the sum column. If the sum equals or exceeds 2, note down the remainder in the sum column and carry over the quotient (1) to the next column.
• Step 3: Proceed to the next column towards the left, adding the two bits alongside any carryover from the preceding column. Once more, if the sum is 1 or less, record it in the sum column; if it surpasses 2, write down the remainder in the sum column and carry over the quotient to the subsequent column.
• Step 4: Continue this iterative process for each successive column until all bits are added.
• Step 5: Should the sum of the last two bits result in a carryover, introduce an extra bit on the left side of the sum to indicate the carryover.
• Step 6: Validate the sum to ensure it fits within 8 bits. If it exceeds 8 bits, additional bits are necessary to represent the sum accurately.

Adding Binary Walkthrough

• In this binary addition example, we start by adding the two least significant bits (LSBs): 0 + 0 = 0. This result is then written down in the sum column.
• Next, we move to the adjacent column on the left and calculate the sum of the two bits along with the carryover from the previous column: 1 + 1 + 0 = 10.
• We record the remainder of this sum (which is 0) in the sum column and carry over the quotient (1) to the next column.
• This process is repeated for the following two columns, eventually resulting in the sum 101110000.

Overflow

• An overflow error occurs when the result of a binary addition exceeds the maximum value that can be represented. In an 8-bit system, the highest value is 255.
• Overflow happens when adding two numbers produces a carry bit that cannot be stored.
• To prevent overflow errors, it is crucial to verify that the result of binary addition stays within the representable range.
• Overflow errors are not limited to addition; they can also arise in operations like multiplication or division.