← ACARA Digital Technologies Years 7–8

Checking a conversion by converting back

Check a decimal to binary answer by reading the binary back into decimal, adding the place values, and comparing with the starting number. If they match, it is right.

Part of: ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 22

Understanding Checking a conversion by converting back in ACARA Digital Technologies Years 7–8

What it does: The 1s in 1010 sit under 8 and 2. They add to 10, which matches the starting number, so the answer is correct. Going to binary and then back again should land on the number you started with, which is a check in both directions. Converting back means adding place values such as 8, 4, 2 and 1 wherever there is a 1. A correct conversion always gives back the same number. A mismatch is a warning sign that something went wrong. Only add the place values that have a 1. In 10110 those are 16, 4 and 2, which total 22.

Common mistakes: 13 is 8 + 4 + 1, which is 1101 in binary. 1110 is 14, so reading it back gives 14 and not 13. Line 2 should be binary ← 1101. The binary 1010 reads back as 8 + 2 = 10. The starting number must be 10 for the check to match. Line 1 should be number ← 10.

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This module's key terms are also in a printable crossword (Modules 189–203) and word search (Modules 189–236).

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Learning
Duo
You converted 13 to binary and got 1101. Which check shows it is right?
Count the digits: there are 4 of them, so it must be rightAdd the place values: 8 + 4 + 0 + 1 = 13, which matches
Matches
Start 12, answer 1011, back 8 + 2 + 1 = 11, so it is right
↓
The converted-back number is 11, not 12. They do not match, so the answer is wrong, and it should be 1100.
Applying
Meanings
Term
convert back
Meaning
Check a decimal to binary answer by reading the binary back into decimal, adding the place values, and comparing with the starting number. If they match, it is right.
Practice
=IF(1*64+0*32+0*16+0*8+0*4+0*2+1*1=B3,"Match","Wrong")
Testing
Gaps
=(DEC2BIN(13))
Check Answer
Spots
1number ← 13
2binary ← 1110

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Quick Questions

1. You converted 13 to binary and got 1101. Which check shows it is right?
A. Add the place values: 8 + 4 + 0 + 1 = 13, which matches ✓
B. Count the digits: there are 4 of them, so it must be right
Read the binary back into decimal by adding the place values that have a 1. If the total matches the starting number, the answer is right.
2. A student converts 10 to binary and writes 1001. What happens when you read it back?
A. 8 + 1 = 9, which is not 10, so the answer is wrong ✓
B. 8 + 1 = 10, so the answer is right
1001 has a 1 in the 8s place and the 1s place, which makes 9. The correct answer for 10 is 1010.
3. What is the first step when you convert a binary answer back to decimal?
A. Divide the binary number by 2 again
B. Write the place values above each bit, then add the ones that have a 1 ✓
Converting back means adding place values such as 8, 4, 2 and 1 wherever there is a 1.
4. You convert back and get a different number from the one you started with. What does that tell you?
A. The conversion is fine because the numbers can differ
B. There is a mistake somewhere, so try the conversion again ✓
A correct conversion always gives back the same number. A mismatch is a warning sign that something went wrong.
5. You converted 22 to 10110. Which sum checks the answer?
A. 16 + 4 + 2 = 22 ✓
B. 16 + 8 + 4 + 2 = 30
Only add the place values that have a 1. In 10110 those are 16, 4 and 2, which total 22.

Match the Pairs

1101 → 8 + 4 + 0 + 1 = 13 → Reading the binary back into decimal by adding the place values that have a 1
Start 13, back 13, match → The converted-back number equals the starting number, so the conversion is correct
To check that 10 was converted to 1010, add the place values of the 1s and compare with 10 → 8 + 2 = 10
Checking works in both directions: convert decimal to binary, then binary back to decimal → DEC2BIN(9) = 1001, BIN2DEC(1001) = 9
Start 12, answer 1011, back 8 + 2 + 1 = 11, so it is right → The converted-back number is 11, not 12. They do not match, so the answer is wrong, and it should be 1100.
Start 6, answer 110, back 4 + 2 + 1 = 7, so it matches → The 1s are under 4 and 2 only, so the total is 6, not 7. The place value 1 was added by mistake because there is a 0 in that column.

Key Term

convert back
Check a decimal to binary answer by reading the binary back into decimal, adding the place values, and comparing with the starting number. If they match, it is right.

Fill in the Blanks

1. =BIN2DEC(DEC2BIN(13))
Hint: Type the function that reads binary text back into a denary number, which checks the conversion.
2. =BIN2DEC(DEC2BIN(13))
Hint: Type the function that does the first conversion, from denary to binary, before you convert back.
3. 1101 = 8 + 4 + 0 + 1 = 13
Hint: Add the place values to find the total, then compare it with the starting number.
4. back ← BIN2DEC(answer) IF back = start THEN OUTPUT "Correct"
Hint: Type the comparison operator that checks whether the converted-back number matches the starting number.
5. =IF(BIN2DEC(DEC2BIN(A1))=A1,"Right","Wrong")
Hint: Type the function that chooses between two results, so a wrong conversion can be spotted.

Spot the Error

Question 1
A number ← 13
B binary ← 1110
C total ← 8 + 4 + 0 + 1
D OUTPUT total = number
Line B — 13 is 8 + 4 + 1, which is 1101 in binary. 1110 is 14, so reading it back gives 14 and not 13. Line 2 should be binary ← 1101.
Question 2
A number ← 12
B binary ← 1010
C total ← 8 + 0 + 2 + 0
D OUTPUT total = number
Line A — The binary 1010 reads back as 8 + 2 = 10. The starting number must be 10 for the check to match. Line 1 should be number ← 10.
Question 3
A number ← 6
B binary ← 110
C total ← 4 + 2 + 0
D IF total ≠ number THEN
E OUTPUT "Correct"
Line D — The check should say Correct when the total from reading the binary back equals the starting number. Here 4 + 2 + 0 = 6, which matches, so the test must use =, not ≠. Line 4 should be IF total = number THEN.
Question 4
A binary ← 101
B places ← 3, 2, 1
C total ← 4 + 0 + 1
D OUTPUT total
Line B — Binary place values double each time: 4, 2, 1. Using 3, 2, 1 gives the wrong total when you read the number back. Line 2 should be places ← 4, 2, 1.
Question 5
A number ← 11
B binary ← 1011
C total ← 8 + 4 + 2 + 1
D OUTPUT total = number
Line C — The 0 in 1011 is in the 4s place, so add 0 and not 4. The total should be 8 + 0 + 2 + 1 = 11. Adding 4 gives 15, which does not match.

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