Converting binary to hexadecimal using nibbles
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. How do you split a binary number into nibbles before converting it to hex?
2. Which is the hex value of 1010 1111?
3. Convert 11010 to hex. Which is correct?
4. How many hex digits does an 8-bit binary number give?
5. How many hex digits does a 16-bit binary number give?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 11011 0110 → B6 | AGroup from the right, then pad the left group with leading zeros so it has 4 bits. | |
| 211010 → 0001 1010 | B1111 → F | |
| 3A 16-bit binary number is split into four nibbles, so it gives 4 hex digits. | CThe nibble 1101 was converted to the denary number 13 rather than the single hex digit D. | |
| 4Nibble 1111 is worth 8 + 4 + 2 + 1 = 15, which is the hex digit F. | D1010 1111 0000 0011 → AF03 | |
| 510110110 → 101 10110 → 5 16 | EEach 4-bit nibble becomes one hex digit: 1011 is B and 0110 is 6, so an 8-bit number gives 2 hex digits. | |
| 61101 0011 → 13 3 | FThe bits were split into groups from the left, not from the right, and the groups are not 4 bits long. |
C
Definitions
binary to hex
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
1010 0011 in hex is _3
2.
101101 padded to 8 bits = __101101
3.
8-bit binary gives _ hex digits
4.
1111 0000 1010 0001 = F0_1
5.
Split the bits into groups of _
from the right
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
Binary: 11010110
B
Nibbles: 110 10110
C
1101 = 13 = D, 0110 = 6
D
Hex: D6
Question 2
A
Binary: 00101111
B
Nibbles: 0010 1111
C
0010 = 2
D
1111 = 15 = E
E
Hex: 2F
Question 3
A
Binary: 101101
B
Pad: 10110100
C
Nibbles: 0010 1101
D
Hex: 2D
Question 4
A
Binary: 10101010
B
Nibbles: 1010 1010
C
Hex digits: 4
D
1010 = 10 = A
E
Hex: AA
Question 5
A
Binary: 0001001010111100
B
Nibbles: 0001 0010 1011 1100
C
16 bits = 4 hex digits
D
0001=1 0010=2 1011=A 1100=C
E
Hex: 12BC
Answer Key
Converting binary to hexadecimal using nibbles
Section A: Quick Questions
Q1
A — Groups of four bits, starting from the right
Q2
A — AF
Q3
B — 1A (pad to 0001 1010)
Q4
B — 2 hex digits
Q5
A — 4 hex digits
Section B: Match the Pairs
Q1
1011 0110 → B6 → Each 4-bit nibble becomes one hex digit: 1011 is B and 0110 is 6, so an 8-bit number gives 2 hex digits.
Q2
11010 → 0001 1010 → Group from the right, then pad the left group with leading zeros so it has 4 bits.
Q3
A 16-bit binary number is split into four nibbles, so it gives 4 hex digits. → 1010 1111 0000 0011 → AF03
Q4
Nibble 1111 is worth 8 + 4 + 2 + 1 = 15, which is the hex digit F. → 1111 → F
Q5
10110110 → 101 10110 → 5 16 → The bits were split into groups from the left, not from the right, and the groups are not 4 bits long.
Q6
1101 0011 → 13 3 → The nibble 1101 was converted to the denary number 13 rather than the single hex digit D.
Section C: Definitions
Q1
binary to hex — Split the bits into groups of four from the right (nibbles), pad the left group with zeros if needed, then replace each nibble with its hex digit.Section D: Fill in the Blanks
Q1
1010 0011 in hex is A3Q2
101101 padded to 8 bits = 00101101Q3
8-bit binary gives 2 hex digitsQ4
1111 0000 1010 0001 = F0A1Q5
Split the bits into groups of 4
from the rightSection E: Spot the Error
Q1
B — Bits must be split into groups of four from the right. 11010110 becomes 1101 0110, not 110 10110.
Q2
D — 1111 is 15 in denary, which is F in hex. E is 14. It should be 1111 = 15 = F.
Q3
B — Padding zeros go on the left of the number so its value does not change. It should be 00101101.
Q4
C — An 8-bit number has two nibbles, so it gives 2 hex digits, not 4.
Q5
D — 1011 is 11 in denary, which is B in hex. A is 10. It should be 1011=B.