➕ Component 1 · 1.2 Data Representation
1.2.4b Binary Addition & Overflow
OCR J277 · GCSE Computer Science · ~10 min read
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Video
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Worksheet
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Quiz

Binary Addition Rules

Binary addition works like denary addition but uses only 0s and 1s. There are only four rules to remember:

AdditionResultCarry
0 + 000
0 + 110
1 + 010
1 + 101 (carry 1)
1 + 1 + 1 (with carry)11 (carry 1)

The key rule: 1 + 1 = 10 in binary (denary 2). You write 0 and carry 1 to the next column.

Worked Example 1: 00110101 + 00011011

Add these two 8-bit binary numbers:

1286432168421
Number 100110101
Number 200011011
Carry01111110
Result01010000

Check: 00110101 = 53, 00011011 = 27, 53 + 27 = 80 = 01010000 ✓

Worked Example 2: 11001010 + 00101100

1286432168421
Number 111001010
Number 200101100
Carry00010000
Result11110110

Check: 202 + 44 = 246 = 11110110 ✓

Overflow

Overflow occurs when the result of a binary addition is too large to be stored in the available number of bits. With 8 bits, the maximum value is 255 (11111111). If the result exceeds 255, a carry is generated beyond the MSB — this carry is lost (as there are no more bits to hold it), and the result stored is incorrect.

Overflow Example: 11110000 + 00110000

11110000 = 240, 00110000 = 48. 240 + 48 = 288 — but 288 > 255, so overflow occurs.

1286432168421Carry out
Number 111110000
Number 200110000
Result001000001 (lost!)

The 8-bit result is 00100000 = 32 — this is wrong because the carry bit has been lost. This is overflow. The correct answer (288) cannot be stored in 8 bits.

Detecting and Handling Overflow

  • A carry out of the MSB position is the overflow flag — it signals that the result is too large
  • Computers use an overflow flag in the status register to signal this error
  • To avoid overflow, use more bits (e.g. 16-bit or 32-bit numbers instead of 8-bit)
Exam tip: When adding binary numbers in an exam, always work from right to left (LSB to MSB). Show carry bits clearly above each column. If a carry is generated from the MSB column, state that this is overflow and the result is incorrect. You will get marks for identifying overflow even if your arithmetic has a small error elsewhere.
⚠️ Common Mistakes
  • Forgetting the carry — the most common error. A carry from column 1 must be added to column 2
  • Working left to right instead of right to left (start at the LSB)
  • Confusing overflow with a wrong answer — overflow is a specific condition where the carry exits the MSB
  • Writing "10" as two digits instead of carrying — 1+1=10 means write 0 carry 1
  • Not checking your answer: convert result back to denary to verify
✅ Notes completed!
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Video coming soon

What's in this video

  • • The four binary addition rules (0+0, 0+1, 1+1, 1+1+carry)
  • • Step-by-step column addition with carry tracking
  • • What overflow is and when it occurs
  • • How to identify overflow in exam questions
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Worksheet — 1.2.4b Binary Addition & Overflow

8 questions · 20 marks · Show all working including carry bits

Q1State the result of 1 + 1 in binary. What happens to the carry?[2]
✅ Mark scheme
1 + 1 = 10 in binary (write 0, carry 1) [1]; the carry is passed to the next (higher value) column [1].
Q2Add 00110011 + 00001010. Show carry bits and give the result in binary and denary.[3]
✅ Mark scheme
51 + 10 = 61. Binary: 00111101. [1 method showing carries, 1 correct binary result, 1 denary check].
Q3Add 01100100 + 00011001. Show your working.[2]
✅ Mark scheme
100 + 25 = 125 = 01111101. [1 for method, 1 for correct result].
Q4What is overflow in the context of binary addition? Give the condition that causes it.[2]
✅ Mark scheme
Overflow is when the result of binary addition is too large to be stored in the given number of bits [1]; it occurs when a carry is generated out of the most significant bit (MSB) position [1].
Q5Add 11000000 + 01000001. Does overflow occur? Explain.[3]
✅ Mark scheme
192 + 65 = 257 > 255 so overflow occurs [1]; carry out of MSB = 1 [1]; 8-bit result is 00000001 which is incorrect — the carry (= 256) is lost [1].
Q6Add 10101010 + 01010110. Show working and state whether overflow occurs.[3]
✅ Mark scheme
170 + 86 = 256 → overflow occurs [1]; carry out of MSB [1]; 8-bit result is 00000000, which is incorrect [1].
Q7State one way that a computer can handle overflow when adding 8-bit numbers.[2]
✅ Mark scheme
Use more bits to store the result, e.g. 16-bit or 32-bit numbers [1]; or set an overflow flag in the status register to signal the error to the CPU [1].
Q8A student adds two 8-bit binary numbers: 11111111 + 00000001. What is the 8-bit result? Is it correct? Explain.[3]
✅ Mark scheme
255 + 1 = 256; 8-bit result is 00000000 [1]; this is NOT correct [1]; overflow has occurred — a carry is generated out of the MSB, and the result (256) cannot be stored in 8 bits [1].
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Mini Test — 1.2.4b Binary Addition & Overflow

10 questions · 10 marks · 10 minutes

  • • 5 multiple choice + 5 short answer
  • • Show carries in addition questions
← 1.2.4a Binary & Denary 1.2 Data Representation 1.2.4c Binary Shifts →
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