Binary addition is tested on every data representation question. You need to add two binary numbers column by column, carry correctly, and identify when overflow has occurred. No calculator permitted — this must be done from memory.
🛠️ Open Binary Converter →How to identify overflow in the exam:
If there is a carry out of the leftmost (8th) column — i.e. the result would need a 9th bit — then overflow has occurred. State this explicitly: "Overflow has occurred because a carry was generated out of the most significant bit."
Try these before expanding the hints. Write your answer, then compare.
Add the following 8-bit binary numbers and state whether overflow has occurred: 10110011 + 01101010
Mark scheme hint: 10110011 + 01101010 ────────── 100011101 Result: 100011101 (9 bits) [1]. Stored 8-bit result: 00011101 [1]. Overflow HAS occurred because a carry was generated out of the most significant bit [1].
Explain what is meant by overflow in the context of binary addition.
Mark scheme hint: Overflow occurs when the result of a binary addition is too large to be represented in the available number of bits [1]; this is indicated by a carry out of the most significant (leftmost) bit, and the stored result will be incorrect [1].
A logical shift left is applied to the 8-bit value 00001010. State the result and what arithmetic operation this is equivalent to.
Mark scheme hint: Result: 00010100 [1]; equivalent to multiplying by 2 (00001010 = 10 in denary, 00010100 = 20 in denary) [1].
Convert 47 to binary. Show your working.
Mark scheme hint: 47 = 32+8+4+2+1 = 00101111 [1]. Method mark for showing column headers or repeated division [1].
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Question Bank →Writing the carry below the line and then forgetting to include it in the next column.
Write carries ABOVE the column you are about to add, not below. Mark: "carry 1" directly above the next column before adding that column. This prevents forgetting carries.
Saying "overflow occurs when the number is negative" — this confuses overflow with signed numbers.
Overflow in binary addition occurs when the result needs MORE BITS than are available — shown by a carry out of the leftmost (most significant) bit. The stored result is numerically wrong because a bit has been lost.
"A left shift multiplies by 10" — confusing binary shift with denary.
A logical shift LEFT multiplies by 2 (not 10). This is because moving all bits one place left doubles the binary value. A shift right divides by 2. Shift left by 3 = multiply by 2³ = multiply by 8.
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0 + 0 = 0. 0 + 1 = 1. 1 + 0 = 1. 1 + 1 = 0 carry 1. 1 + 1 + 1 (when adding with a carry) = 1 carry 1. Work from right to left, exactly like denary addition, but using only 0 and 1.
Overflow occurs when the result of a binary addition is too large to be stored in the available number of bits. For example, if you add two 8-bit numbers and the result requires a 9th bit, overflow has occurred. In the exam: if there is a carry OUT of the most significant bit (MSB), overflow has occurred. The stored result will be incorrect.
The method is identical — work column by column from right to left. For each column, add the two bits plus any carry from the previous column, write down the result and carry forward any overflow. The column rules never change regardless of how many bits you are working with.
A logical shift left moves all bits one position to the left, inserting a 0 on the right. This is equivalent to multiplying by 2. A logical shift right moves all bits right, inserting a 0 on the left — equivalent to integer division by 2. Shifting left by n positions multiplies by 2ⁿ; shifting right by n positions divides by 2ⁿ.