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J277 1.2.4 Binary addition and overflow

Part 4 of 5 · J277 1.2.4 · Number systems

Adding binary numbers directly with the column method, and what happens when the answer will not fit.

Students will:

  • recall the four binary addition facts
  • add two binary numbers using the column method
  • record carries clearly
  • explain what an overflow error is
  • recognise when an answer needs more than 8 bits

Inside: 6 text sections, 2 multiple-choice activities, 2 completion activities, 1 written answer, 4 number activities. 23 marks. Suggested teaching time: 40–60 minutes. 1 diagram.

Includes a teacher guide with suggested sections, timings and common misconceptions.

Series: J277 1.2.4 · Number systems, part 4 of 5.

Shared by Coding PathwayVerified teacher

  • 15 cells
  • About 45 minutes
  • CC BY-SA 4.0
  • Shared 17 Aug 2026
  • Updated 27 Oct 2026

Preview

The whole resource, exactly as a class sees it. Answers and marking are held back.

Binary addition and overflow

Add binary numbers one column at a time. You will show carries, then decide whether a complete result fits into eight bits.

1. Column facts

Binary additionResultWhat to write
0 + 00Write 0.
0 + 11Write 1.
1 + 110Write 0; carry 1 left.
1 + 1 + 111Write 1; carry 1 left.

Binary 10 means denary 2. Binary 11 means denary 3. Begin at the right, including any carry from the previous column.

Fill in the blanks4 marks
In binary, 0 + 0 = Answer 1, 0 + 1 = Answer 2, 1 + 1 = Answer 3, and 1 + 1 + 1 = Answer 4.
  • 0
  • 1
  • 2
  • 10
  • 11
  • 100

2. See each carry

For 0101 + 0011, work right to left. The first three columns each total binary 10: write 0 and carry 1. The last column totals 1. The result is 1000.

Put a carry above the column it enters. An unused carry box may be left blank or contain 0.

Binary column addition with carries A four-bit worked example adds 0101 and 0011 to make 1000. Carries of one enter the 8, 4 and 2 columns. The rightmost column has no incoming carry. A carry enters the next column 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 + Carries Start at the right: 1 + 1 = 10. Write 0; carry 1 one column left.
Number systems4 marks

Add these four-bit values and show every carry.

a)Add these 4-bit binary numbers: 0110 + 0011.

Carries
First number
0110
Second number
0011
Total

b)Add these 4-bit binary numbers: 0101 + 0110.

Carries
First number
0101
Second number
0110
Total

3. Extend to eight bits

The method stays the same: add from the right, include an incoming carry, write the new answer bit, and carry left when the column totals 2 or 3. Continue through all eight columns.

Converting through denary can check your result, but does not show binary column working.

Number systems4 marks

Add each eight-bit pair and show every carry.

a)Add these 8-bit binary numbers: 00110101 + 01001110.

Carries
First number
00110101
Second number
01001110
Total

b)Add these 8-bit binary numbers: 01011011 + 00100111.

Carries
First number
01011011
Second number
00100111
Total
Multiple choice1 mark

A column totals 1 + 1. Why is a 1 carried into the next column?

  • AEvery column must contain a carry
  • BBinary 10 has 0 in this column and 1 in the next place value
  • CThe final answer is always 1
  • DA carry turns the number into denary

4. When the result does not fit

Eight bits can represent 0–255. An overflow error occurs when the complete result needs more bits than are available.

11111111 + 00000001 = 100000000: the complete result is 256 and needs nine bits. An eight-bit register cannot keep the extra bit.

Carries inside the eight columns are normal. A carry beyond the left edge means this eight-bit result has overflowed. The next grid shows only the eight stored answer bits. A separate question checks whether the full result fits.

Number systems2 marks

Enter the eight stored answer bits for each addition. Keep only eight positions in this grid.

a)Add these 8-bit binary numbers: 10100100 + 01110000.

Carries
First number
10100100
Second number
01110000
Total

b)Add these 8-bit binary numbers: 00101010 + 00010101.

Carries
First number
00101010
Second number
00010101
Total
Multiple choice1 mark

An eight-bit register adds 00101010 and 00010101. Which statement is correct?

  • AAny carry means that the addition overflows
  • BThe complete result is 63, which fits within eight bits
  • CEvery addition of two bytes needs nine result bits
  • DThe answer overflows because it contains 1 bits
Fill in the blanks1 mark
For 10100100 + 01110000, write the complete binary total before restricting it to eight bits: Answer 1.
Written answer2 marks

Explain why adding 10100100 and 01110000 causes an overflow error in an eight-bit register.

Students type their answer here.

Number systems4 marks

Complete these eight-bit additions, showing all carries.

a)Add these 8-bit binary numbers: 01010110 + 00111001.

Carries
First number
01010110
Second number
00111001
Total

b)Add these 8-bit binary numbers: 01101001 + 01010011.

Carries
First number
01101001
Second number
01010011
Total

Review

Choose one addition to check. Compare the final answer and carry row separately, then explain whether its full result fits within the stated width.