Adding two 8-bit binary integers
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. Which column do you start with when adding two binary numbers?
2. What do you do when a column adds up to 1 + 1?
3. Where do you write a carry bit?
4. How should you line up two 8-bit numbers before adding?
5. What is 1 + 1 + a carried 1 in a single column?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 100000101 + 00000011 = 00001000 | AThe carry from the right-hand column was never added to the next column. Carrying every 1 gives 00000100 (3 + 1 = 4). | |
| 21 + 1 = 10 | B00001010 + 00000110 = 00010000, so 10 + 6 = 16 | |
| 3Check a binary addition by converting both numbers to denary and adding them | C2 is not a binary digit. 1 + 1 must be written as 10: write 0 and carry 1. | |
| 4Two 1s plus a carried 1 make 3, so write 1 in the column and carry 1 left | DAdds 5 and 3 in binary to give 8, working column by column from the right | |
| 500000011 + 00000001 = 00000010 | EWrite 0 in this column and carry 1 to the next column on the left | |
| 61 + 1 = 2 | F1 + 1 + 1 = 11 |
C
Definitions
binary addition
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
00000101
+ 00000011
________
2.
1 + 1 = __
3.
1 + 1 + 1 = __
4.
00001010 + 00000101: 10 + 5 = __
5.
Add from the right, carry to the ____
E
Spot the Error
Shade in the letter of the line that contains an 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)
Question 2
A
00001100 (12)
B
+ 0000111 (7)
C
00010011 (19)
D
Check: 12 + 7 = 19
Question 3
A
Check: 9 + 6 = 16
B
00001001 + 00000110
C
= 00001111
D
00001111 is 15, so it matches
Question 4
A
Carries: 00001110
B
A: 00000111
C
B: 00000001
D
Sum: 00001100
Question 5
A
A = 01100100 (100)
B
B = 00110010 (50)
C
A + B = 10011010 (154)
D
Check: 100 + 50 = 150
Answer Key
Adding two 8-bit binary integers
Section A: Quick Questions
Q1
B — The rightmost column
Q2
B — Write 0 and carry 1
Q3
A — Above the next column to the left
Q4
A — Right-aligned, with bits of the same place value in the same column
Q5
A — Write 1 and carry 1
Section B: Match the Pairs
Q1
00000101 + 00000011 = 00001000 → Adds 5 and 3 in binary to give 8, working column by column from the right
Q2
1 + 1 = 10 → Write 0 in this column and carry 1 to the next column on the left
Q3
Check a binary addition by converting both numbers to denary and adding them → 00001010 + 00000110 = 00010000, so 10 + 6 = 16
Q4
Two 1s plus a carried 1 make 3, so write 1 in the column and carry 1 left → 1 + 1 + 1 = 11
Q5
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).
Q6
1 + 1 = 2 → 2 is not a binary digit. 1 + 1 must be written as 10: write 0 and carry 1.
Section C: Definitions
Q1
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.Section D: Fill in the Blanks
Q1
00000101
+ 00000011
00001000Q2
1 + 1 = 10Q3
1 + 1 + 1 = 11Q4
00001010 + 00000101: 10 + 5 = 15Q5
Add from the right, carry to the leftSection E: Spot the Error
Q1
D — The carry from column 2 was ignored. Column 3 is 1 + 0 + 1 (the carried 1) = 10, so write 0 and carry 1.
Q2
B — The second number has only 7 digits, so its columns do not line up. It must be written as 8 bits: 00000111.
Q3
A — 9 + 6 = 15, not 16. The denary check must give 15 to match the binary answer 00001111.
Q4
D — Following the carries, 7 + 1 = 8, which is 00001000 in binary. 00001100 is 12.
Q5
C — Adding column by column gives 10010110, which is 150. 10011010 is 154, so it fails the denary check.