Common mistakes when converting between decimal and binary
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. A student converts 6 to 3-bit binary. Which answer is correct?
2. Which list shows binary place values going from the right-hand bit to the left?
3. Write 9 in binary. Which answer is correct?
4. Write 5 as a 4-bit binary number. Which answer is correct?
5. Dividing 13 by 2 again and again gives remainders 1, 0, 1, 1 in the order you find them. How do you read them?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 11001 written as 101 | A6/2=3 r0, 3/2=1 r1, 1/2=0 r1 -> 110 | |
| 21201 | BInvalid binary: 2 is not a binary digit | |
| 3Binary place values start at 1 on the right and double as you move left | CA middle zero was dropped, so 9 became 5 | |
| 4When dividing by 2, read the remainders from bottom to top to get the binary number | DThe place values started from the left end. The 1 place belongs on the right, so 110 = 1x4 + 1x2 + 0x1 = 6. | |
| 5110 = 1x1 + 1x2 + 0x4 = 3 | E8 4 2 1 | |
| 65 in 8-bit binary: 101 | FThe leading zeros are missing. In 8 bits, 5 should be written 00000101. |
C
Definitions
binary conversion mistake
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
Place values right to left: 1, 2, 4, _
2.
Read remainders from ______ to top
3.
9 = 8 + 1, so 4-bit binary is 1_01
4.
Binary 1021 is wrong because of the digit _
5.
Remainders down: 1, 0, 1, 1
Read upwards: ____
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
Binary 1101 to decimal
B
Place values: 1 2 4 8
C
8 + 4 + 0 + 1 = 13
D
Answer: 13
Question 2
A
Convert 6 to 3-bit binary
B
6 = 4 + 2 so 4s=1, 2s=2
C
1s place = 0
D
Answer: 110
Question 3
A
Convert 6 to binary
B
6 / 2 = 3 remainder 0
C
3 / 2 = 1 remainder 1
D
Read remainders top to bottom
E
Answer: 110
Question 4
A
9 = 8 + 1 = 101 in binary
B
As 8 bits: 00001001
C
Four zeros pad it to 8 bits
Question 5
A
10 / 2 = 5 remainder 0
B
5 / 2 = 2 remainder 1
C
2 / 2 = 1 remainder 0
D
1 / 2 = 0 remainder 2
E
Bottom to top: 1010
Answer Key
Common mistakes when converting between decimal and binary
Section A: Quick Questions
Q1
A — 110
Q2
A — 1, 2, 4, 8
Q3
A — 1001
Q4
B — 0101
Q5
B — Bottom to top: 1101
Section B: Match the Pairs
Q1
1001 written as 101 → A middle zero was dropped, so 9 became 5
Q2
1201 → Invalid binary: 2 is not a binary digit
Q3
Binary place values start at 1 on the right and double as you move left → 8 4 2 1
Q4
When dividing by 2, read the remainders from bottom to top to get the binary number → 6/2=3 r0, 3/2=1 r1, 1/2=0 r1 -> 110
Q5
110 = 1x1 + 1x2 + 0x4 = 3 → The place values started from the left end. The 1 place belongs on the right, so 110 = 1x4 + 1x2 + 0x1 = 6.
Q6
5 in 8-bit binary: 101 → The leading zeros are missing. In 8 bits, 5 should be written 00000101.
Section C: Definitions
Q1
binary conversion mistake — A slip such as reversing place values, dropping a zero, reading remainders top to bottom or using a 2. Binary only uses 0 and 1, and remainders are read bottom to top.Section D: Fill in the Blanks
Q1
Place values right to left: 1, 2, 4, 8Q2
Read remainders from bottom to topQ3
9 = 8 + 1, so 4-bit binary is 1001Q4
Binary 1021 is wrong because of the digit 2Q5
Remainders down: 1, 0, 1, 1
Read upwards: 1101Section E: Spot the Error
Q1
B — The place values were written from the wrong end. In binary the leftmost bit has the biggest value, so they should be 8 4 2 1.
Q2
B — A binary digit can only be 0 or 1. The 2s place needs one 2, so it holds the digit 1, not the digit 2.
Q3
D — Remainders must be read from bottom to top. Reading them top to bottom gives 011, which is the wrong order. It should be 110.
Q4
A — A middle zero was dropped. The 4s and 2s places are both 0, so 9 is 1001, not 101.
Q5
D — When you divide by 2 the remainder can only be 0 or 1. 1 / 2 gives 0 remainder 1, and that 1 is the top bit of 1010.