← IGCSE Computer Science Paper 1

Adding two 8-bit binary integers

Add two 8-bit binary numbers column by column from the right. Carry any 1 to the next column on the left. 1 + 1 = 10, so write 0 and carry 1. Check by adding the denary values.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 22, IGCSE Computer Science 0478 — 2.2 Methods of Error Detection — Module 23

Understanding Adding two 8-bit binary integers in IGCSE Computer Science Paper 1

What it does: 01010 is 10 and 00110 is 6. Their denary sum is 16, which matches 00010000, so the answer is correct. A column holding two 1s and a carry adds up to 3, which is 11 in binary. Write the right-hand 1 and carry the left-hand 1. Each column must have the same place value in both numbers (1s, 2s, 4s and so on), so line them up from the right. Checking in denary: 5 + 3 = 8, and 8 in binary is 00001000. The carries ripple left through the 1s and 2s columns. Check in denary: 10 + 6 = 16, and 16 is 00010000 in binary. 00001100 is 12, so it does not match.

Common mistakes: The carry from column 2 was ignored. Column 3 is 1 + 0 + 1 (the carried 1) = 10, so write 0 and carry 1. The second number has only 7 digits, so its columns do not line up. It must be written as 8 bits: 00000111.

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Learning
Duo
Which column do you start with when adding two binary numbers?
The rightmost columnThe leftmost column
Matches
00000011 + 00000001 = 00000010
↓
The carry from the right-hand column was never added to the next column. Carrying every 1 gives 00000100 (3 + 1 = 4).
Applying
Meanings
Term
binary addition
Meaning
Add two 8-bit binary numbers column by column from the right. Carry any 1 to the next column on the left. 1 + 1 = 10, so write 0 and carry 1. Check by adding the denary values.
Practice
01111110
Testing
Gaps
Check Answer
Spots
3Col 2: 0 + 1 + 1 = 0 carry 1
4Col 3: 1 + 0 = 1 carry 0

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Quick Questions

1. Which column do you start with when adding two binary numbers?
A. The leftmost column
B. The rightmost column ✓
Start at the right (the least significant bit) and work left, just like denary addition. Any carry then moves to the next column on the left.
2. What do you do when a column adds up to 1 + 1?
A. Write 2 and carry nothing
B. Write 0 and carry 1 ✓
Binary only has the digits 0 and 1. 1 + 1 = 10 in binary, so write 0 in this column and carry 1 to the next column.
3. Where do you write a carry bit?
A. Above the next column to the left ✓
B. Above the next column to the right
A carry moves towards the more significant bits, so it goes above the column to the left, where it is added in.
4. How should you line up two 8-bit numbers before adding?
A. Right-aligned, with bits of the same place value in the same column ✓
B. Left-aligned, starting from the first digit written
Each column must have the same place value in both numbers (1s, 2s, 4s and so on), so line them up from the right.
5. What is 1 + 1 + a carried 1 in a single column?
A. Write 1 and carry 1 ✓
B. Write 0 and carry 1
1 + 1 + 1 = 3, which is 11 in binary. Write the right-hand 1 and carry the other 1 to the next column.

Match the Pairs

00000101 + 00000011 = 00001000 → Adds 5 and 3 in binary to give 8, working column by column from the right
1 + 1 = 10 → Write 0 in this column and carry 1 to the next column on the left
Check a binary addition by converting both numbers to denary and adding them → 00001010 + 00000110 = 00010000, so 10 + 6 = 16
Two 1s plus a carried 1 make 3, so write 1 in the column and carry 1 left → 1 + 1 + 1 = 11
00000011 + 00000001 = 00000010 → The carry from the right-hand column was never added to the next column. Carrying every 1 gives 00000100 (3 + 1 = 4).
1 + 1 = 2 → 2 is not a binary digit. 1 + 1 must be written as 10: write 0 and carry 1.

Key Term

binary addition
Add two 8-bit binary numbers column by column from the right. Carry any 1 to the next column on the left. 1 + 1 = 10, so write 0 and carry 1. Check by adding the denary values.

Fill in the Blanks

1. 00000101 + 00000011 00001000
Hint: Type the 8-bit binary answer. Add column by column from the right and carry any 1 to the next column.
2. 1 + 1 = 10
Hint: Type the binary result of adding two 1s. It has two digits: write the right one and carry the left one.
3. 1 + 1 + 1 = 11
Hint: Type the binary result of a column with two 1s plus a carried 1. It has two digits.
4. 00001010 + 00000101: 10 + 5 = 15
Hint: Type the denary total of the two denary values. Use it to check the binary sum.
5. Add from the right, carry to the left
Hint: Type the direction a carry moves to the next column.

Spot the Error

Question 1
A Add 00000101 and 00000011
B Col 1: 1 + 1 = 0 carry 1
C Col 2: 0 + 1 + 1 = 0 carry 1
D Col 3: 1 + 0 = 1 carry 0
E Col 4: 0 + 0 + 1 = 1 carry 0
F Answer: 00001000 (8)
Line D — The carry from column 2 was ignored. Column 3 is 1 + 0 + 1 (the carried 1) = 10, so write 0 and carry 1.
Question 2
A 00001100 (12)
B + 0000111 (7)
C 00010011 (19)
D Check: 12 + 7 = 19
Line B — The second number has only 7 digits, so its columns do not line up. It must be written as 8 bits: 00000111.
Question 3
A Check: 9 + 6 = 16
B 00001001 + 00000110
C = 00001111
D 00001111 is 15, so it matches
Line A — 9 + 6 = 15, not 16. The denary check must give 15 to match the binary answer 00001111.
Question 4
A Carries: 00001110
B A: 00000111
C B: 00000001
D Sum: 00001100
Line D — Following the carries, 7 + 1 = 8, which is 00001000 in binary. 00001100 is 12.
Question 5
A A = 01100100 (100)
B B = 00110010 (50)
C A + B = 10011010 (154)
D Check: 100 + 50 = 150
Line C — Adding column by column gives 10010110, which is 150. 10011010 is 154, so it fails the denary check.

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