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1CP2-P-1.3 Binary addition and overflow

Part 3 of 5 · 1CP2-P-1 · Binary foundations

The arithmetic worksheet, teaching column addition first and only then what happens when the answer will not fit.

Students will:

  • apply the four column facts of binary addition
  • add pairs of positive 8-bit integers from right to left
  • tell a carry within the columns apart from overflow out of them
  • decide whether an 8-bit addition overflows
  • explain the consequence of overflow for a stored value

Inside: 10 explanation cells, 2 multiple-choice questions, 3 number cells, 2 fill-in-the-blanks cells and 1 written answer. 18 marks, about 45 minutes.

Series: 1CP2-P-1 · Binary foundations, part 3 of 5.

Shared by Coding PathwayVerified teacher

  • 18 cells
  • About 45 minutes
  • CC BY-SA 4.0
  • Shared 17 Aug 2026

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

Binary addition and overflow

Binary addition uses the same right-to-left column logic as denary addition, but each column contains only 0 or 1. This worksheet separates a carry used during working from overflow beyond the available width.

1. Four column facts

Learn the results as binary patterns:

  • 0 + 0 = 0
  • 0 + 1 = 1
  • 1 + 1 = 10: write 0 and carry 1
  • 1 + 1 + 1 = 11: write 1 and carry 1

The left digit of 10 or 11 moves into the next column as the carry.

Fill in the blanks3 marks
In one binary column, 1 + 1 gives label 1. Write label 2 in the answer row and carry label 3 into the next column.
  • 0
  • 1
  • 10
  • 11

2. Add from right to left

Binary column addition with carriesWork from the rightmost column1 1 1 1 100110110+ 00011101010100111 + 1 = binary 10: write 0 in the column and carry 1 to the next column.The carries support the method; this 8-bit result still fits.

At every column, add the two bits and any incoming carry. Write the answer bit in the same column, then move a carry to the column on its left.

A reverse denary check confirms 54 + 29 = 83, and 01010011 represents 83.

Number systems3 marks

Add each pair of positive 8-bit binary integers.

Complete the answer row and use the carry row. Both totals fit in 8 bits.

a)Add these 8-bit binary numbers: 00110110 + 00011101.

Carries
First number
00110110
Second number
00011101
Total

b)Add these 8-bit binary numbers: 01001111 + 00110101.

Carries
First number
01001111
Second number
00110101
Total

3. A carry is not automatically overflow

The calculation 00110110 + 00011101 contains several carries, yet its result 01010011 fits into eight bits. The carries are ordinary working steps.

Overflow is decided only after comparing the required result with the available storage width and representation.

Multiple choice1 mark

An 8-bit unsigned addition contains a carry in its fourth column, but the final result is 10000100. What can be concluded?

  • AOverflow must have happened because there was a carry.
  • BThe result fits in 8 bits, so that carry alone is not overflow.
  • CThe result is negative because it begins with 1.
  • DBinary addition cannot contain more than one carry.

4. Consolidate the method

Before each calculation:

  1. align both patterns to eight columns;
  2. begin at the right;
  3. include each incoming carry once;
  4. retain leading zeroes in the answer;
  5. check the denary total if useful.
Number systems2 marks

Complete two more positive 8-bit additions.

The carry row is optional working space. Keep exactly eight answer bits.

a)Add these 8-bit binary numbers: 00011011 + 00100110.

Carries
First number
00011011
Second number
00100110
Total

b)Add these 8-bit binary numbers: 01100101 + 00011110.

Carries
First number
01100101
Second number
00011110
Total

5. Overflow

Overflow in an 8-bit location11110000+00110000100100000Available width: 8 bitsRequired width: 9 bitsOVERFLOWOverflow depends on the available width, not merely on seeing a carry during working.

An overflow occurs when the result of a calculation is too large to fit in the location assigned to store it. Here the correct mathematical result needs nine bits, while only eight are available.

The leading ninth bit cannot be represented in that location. Without suitable handling, a program can therefore use or display an incorrect outcome.

Number systems4 marks

Add each pair in an 8-bit unsigned location, then decide whether overflow occurs.

Give the stored 8-bit total and select the reason based on the required width.

a)Add 11110000 and 00110000 in an 8-bit register, then say what happens to the answer.

Carries
First number
11110000
Second number
00110000
Total
Why?

Not answered

b)Add 01100100 and 00101101 in an 8-bit register, then say what happens to the answer.

Carries
First number
01100100
Second number
00101101
Total
Why?

Not answered

6. Explain the consequence

A precise explanation contains a chain:

correct result needs more than 8 bits → assigned location cannot represent it → stored or displayed outcome is not the intended mathematical result

Do not define overflow only as “a number is too big”. State what it is too big for: the available number of bits.

Written answer3 marks

A game stores an unsigned score in 8 bits. The calculation should produce 270. Explain why overflow occurs and describe one effect on the program outcome.

Use the 8-bit range and connect the storage limitation to the observed result.

Students type their answer here.

7. Diagnose before deciding

Use this decision process:

  1. What width is available?
  2. What representation is stated? Here it is unsigned.
  3. What is the full mathematical result?
  4. Does that result fit the permitted range?

A carry within the eight columns may occur in a valid calculation. A carry beyond the most-significant column indicates that this positive unsigned result needs another bit.

Multiple choice1 mark

Which definition of overflow is most precise?

  • AAny calculation that contains a carry.
  • BA result requiring more bits than are available in its assigned location.
  • CAny 8-bit value whose first bit is 1.
  • DA mistake made while converting binary to denary.

Final retrieval

If a positive unsigned addition produces a ninth result bit, the 8-bit location cannot store the complete value. The extra position is the evidence of the width mismatch.

Fill in the blanks1 mark
In an 8-bit positive addition, a complete result requiring a label 1 bit demonstrates overflow.
  • first
  • fourth
  • ninth
  • zero

Ready for signed values

You can now add positive binary patterns, show carries and decide whether an unsigned result fits its stated width.

Next, the same eight bits will be interpreted as signed two's complement. The most-significant place will take a negative value, changing both the range and the meaning of patterns that begin with 1.