Checking a conversion by converting back

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Quick Questions

Shade in the A or B circle for each question.

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

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

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

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

5. You converted 22 to 10110. Which sum checks the answer?

A 16 + 4 + 2 = 22

B 16 + 8 + 4 + 2 = 30

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
11101 → 8 + 4 + 0 + 1 = 13		AThe converted-back number is 11, not 12. They do not match, so the answer is wrong, and it should be 1100.
2Start 13, back 13, match		BThe converted-back number equals the starting number, so the conversion is correct
3To check that 10 was converted to 1010, add the place values of the 1s and compare with 10		CDEC2BIN(9) = 1001, BIN2DEC(1001) = 9
4Checking works in both directions: convert decimal to binary, then binary back to decimal		DReading the binary back into decimal by adding the place values that have a 1
5Start 12, answer 1011, back 8 + 2 + 1 = 11, so it is right		E8 + 2 = 10
6Start 6, answer 110, back 4 + 2 + 1 = 7, so it matches		FThe 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.

Definitions

convert back

Fill in the Blanks

Complete each line of code by filling in the missing parts.

=_______(DEC2BIN(13))

=BIN2DEC(_______(13))

1101 = 8 + 4 + 0 + 1 = __

back ← BIN2DEC(answer) IF back _ start THEN OUTPUT "Correct"

=__(BIN2DEC(DEC2BIN(A1))=A1,"Right","Wrong")

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A number ← 13

B binary ← 1110

C total ← 8 + 4 + 0 + 1

D OUTPUT total = number

Question 2

A number ← 12

B binary ← 1010

C total ← 8 + 0 + 2 + 0

D OUTPUT total = number

Question 3

A number ← 6

B binary ← 110

C total ← 4 + 2 + 0

D IF total ≠ number THEN

E OUTPUT "Correct"

Question 4

A binary ← 101

B places ← 3, 2, 1

C total ← 4 + 0 + 1

D OUTPUT total

Question 5

A number ← 11

B binary ← 1011

C total ← 8 + 4 + 2 + 1

D OUTPUT total = number

Answer Key

Checking a conversion by converting back

Section A: Quick Questions

A — Add the place values: 8 + 4 + 0 + 1 = 13, which matches

A — 8 + 1 = 9, which is not 10, so the answer is wrong

B — Write the place values above each bit, then add the ones that have a 1

B — There is a mistake somewhere, so try the conversion again

A — 16 + 4 + 2 = 22

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

=BIN2DEC(DEC2BIN(13))

1101 = 8 + 4 + 0 + 1 = 13

back ← BIN2DEC(answer)
IF back = start THEN
  OUTPUT "Correct"

=IF(BIN2DEC(DEC2BIN(A1))=A1,"Right","Wrong")

Section E: Spot the Error

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.

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.

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.

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.

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.