Why hexadecimal is used instead of binary

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Quick Questions

Shade in the A or B circle for each question.

1. Why do programmers often write 11111111 as FF?

A FF is shorter and easier to read than 11111111

B The computer stores FF instead of 11111111

2. How many binary bits does ONE hexadecimal digit represent?

A 4 bits

B 8 bits

3. Which statement about copying long values is true?

A Binary is safer to copy because it uses only two digits

B Hex has fewer digits, so there are fewer transcription mistakes

4. Which is the hex value for the 8-bit binary number 10101111?

A FA

B AF

5. Why is converting between hex and binary easier than between denary and binary?

A Each hex digit matches exactly one group of 4 bits

B Hex digits match the same place values as denary

Match the Pairs

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

Left column		Right column
111010110 = D6		AOne hex digit stands for 4 bits, not 8, so 8 bits need just 2 hex digits (F0)
21111 = F		BA5 -> 1010 0101
3Hex has fewer digits than binary, so people make fewer mistakes when copying it		C10111100 -> BC
4Hex converts to binary easily by swapping each digit for its 4-bit group, unlike denary		DComputers still store and process everything as binary; hex is only used by people because it is shorter and easier to read
5Hex is used because computers store data as hex digits instead of binary		EOne hex digit stands for exactly four bits (a nibble)
6One hex digit = 8 bits, so 11110000 = F0 needs 4 hex digits		FThe 8-bit binary value is written with only 2 hex digits, so it is much shorter to read and write

Definitions

hexadecimal

Fill in the Blanks

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

1111 0000 in binary = __ in hex

One hex digit stands for _ bits

10110111 (8 digits) = B7 (_ digits)

0xFF = ____ 1111

Hex converts to binary easier than ______

Spot the Error

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

Question 1

A binary = "11010110"

B nibble1 = "1101"

C nibble2 = "0110"

D hexValue = "6D"

Question 2

A bits = 8

B digits = bits // 2

C print(digits)

Question 3

A binary = "11111111"

B hexa = "FF"

C print(len(binary)) # 8

D print(len(hexa)) # 8

Question 4

A bits_per_hex_digit = 8

B digits = 16 // bits_per_hex_digit

C print(digits)

Question 5

A original = "0110101111010011"

B hexa = "6BD3"

C shorter = len(hexa) > len(original)

D print(shorter)

Answer Key

Why hexadecimal is used instead of binary

Section A: Quick Questions

A — FF is shorter and easier to read than 11111111

A — 4 bits

B — Hex has fewer digits, so there are fewer transcription mistakes

B — AF

A — Each hex digit matches exactly one group of 4 bits

Section B: Match the Pairs

11010110 = D6 → The 8-bit binary value is written with only 2 hex digits, so it is much shorter to read and write

1111 = F → One hex digit stands for exactly four bits (a nibble)

Hex has fewer digits than binary, so people make fewer mistakes when copying it → 10111100 -> BC

Hex converts to binary easily by swapping each digit for its 4-bit group, unlike denary → A5 -> 1010 0101

Hex is used because computers store data as hex digits instead of binary → Computers still store and process everything as binary; hex is only used by people because it is shorter and easier to read

One hex digit = 8 bits, so 11110000 = F0 needs 4 hex digits → One hex digit stands for 4 bits, not 8, so 8 bits need just 2 hex digits (F0)

Section C: Definitions

hexadecimal — A base-16 system that shortens binary. One hex digit stands for four bits, so values are shorter to read, easier to copy without mistakes and quick to convert to and from binary.

Section D: Fill in the Blanks

1111 0000 in binary = F0 in hex

One hex digit stands for 4 bits

10110111 (8 digits) = B7 (2 digits)

0xFF = 1111 1111

Hex converts to binary easier than denary

Section E: Spot the Error

D — The first nibble 1101 is D and the second nibble 0110 is 6, so the hex value is D6, not 6D. The order of the nibbles must be kept.

B — One hex digit stands for four bits, so the number of hex digits is bits // 4, not bits // 2.

D — FF has only 2 hex digits, so len(hexa) is 2. The 8 belongs to the binary version. This shows hex is shorter to read and write.

A — One hex digit stands for 4 bits (a nibble), not 8. The first line should be bits_per_hex_digit = 4.

C — The hex form 6BD3 has 4 digits and the binary has 16, so hex is shorter. The comparison should use < not >.