Cambridge O Level Computer Science · Syllabus 2210 · 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 O Level 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.
Reviewed by Academiq Edu Instructor PanelLast reviewed Syllabus 2026-2028