Cambridge IGCSE Computer Science · Syllabus 0478 · Data Representation
Binary Addition
What is Binary Addition?
Binary addition is the column-by-column addition of binary integers using the rules 0+0=0, 0+1=1 and 1+1=10 carry 1, where a carry out of the leftmost column of a fixed-width register is an overflow.
This definition is part of the Data Representation chapter in Cambridge IGCSE Computer Science.
Binary Addition in context
Binary addition works exactly like denary column addition, but you carry when a column reaches two instead of ten. Align the two numbers so their least significant bits are in the same column, add each column from the right, and carry a 1 into the next column whenever the column total is 2 or 3.
Common mistakes with Binary Addition
- 2. Calling every carry an overflow. Why it fails Carries happen inside almost every binary addition and are completely normal. An overflow error is different: the correct answer is too large for the register to hold. Fix Only the carry out of the leftmost column of an 8-bit unsigned addition signals overflow. See section 1.1 F.
- M4. "Any carry means overflow." Why it fails Carries occur inside almost every binary addition and are ordinary arithmetic. Only a carry out of the leftmost column of the register signals a problem. Correct model Overflow means the correct result lies outside the register's range, not that a column overflowed into the next one. Exam-safe "A carry between columns is normal; an overflow error occurs only when the result is outside the range the register can represent." Test yourselfHideQ. 90 + 45 in an 8-bit register produces four carries. Is that an overflow?A. No — the total 135 is not greater than 255, so it fits.