Binary representation in ARM in ARM Architecture - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to represent the decimal number 5 in 8-bit binary.

ARM Architecture

binary_5 = "00000[1]01"

Drag options to blanks, or click blank then click option'

A2

B0

C1

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using digits other than 0 or 1 in binary representation.

Misplacing the 1 bits in the binary number.

The decimal number 5 in 8-bit binary is 00000101. The blank represents the bit for 4 which is 1.

2fill in blank

medium

Complete the code to show the 8-bit binary representation of the decimal number 10.

ARM Architecture

binary_10 = "[1]1010"

Drag options to blanks, or click blank then click option'

A1100

B0000

C1011

D1010

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing the order of bits.

Using more than 8 bits for the representation.

The 8-bit binary for decimal 10 is 00001010. The blank is for the leading four bits which are 0000 to make it 8 bits.

3fill in blank

hard

Fix the error in the 8-bit binary representation of decimal 13.

ARM Architecture

binary_13 = "0000[1]101"

Drag options to blanks, or click blank then click option'

A1

B0

C2

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 instead of 1 in the blank.

Miscounting the bits in the binary number.

The decimal 13 in binary is 00001101. The blank must be 1 to correctly represent 13.

4fill in blank

hard

Fill both blanks to complete the 8-bit binary representation of decimal 18.

ARM Architecture

binary_18 = "000[1][2]010"

Drag options to blanks, or click blank then click option'

A1

B0

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the bits in the blanks.

Using digits other than 0 or 1.

Decimal 18 in binary is 00010010. The blanks represent the 4th and 5th bits which are 1 and 0 respectively.

5fill in blank

hard

Fill all three blanks to complete the 8-bit binary representation of decimal 29.

ARM Architecture

binary_29 = "000[1][2][3]01"

Drag options to blanks, or click blank then click option'

A1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up the order of bits.

Using 0 where 1 should be and vice versa.

Decimal 29 in binary is 00011101. The blanks represent the 4th, 5th, and 6th bits which are 1, 1, and 1 respectively.

Practice

1. What is the length of a standard binary number used in ARM processors for data representation?

easy

A. 8 bits

B. 16 bits

C. 64 bits

D. 32 bits

Solution

1. Step 1: Understand ARM data size

   ARM processors commonly use 32-bit registers to hold data and instructions.

2. Step 2: Confirm binary length

   Each binary number representing data or instructions in ARM is 32 bits long.

3. Final Answer:

   32 bits -> Option D

4. Quick Check:

   ARM uses 32-bit binary numbers [OK]

Hint: ARM uses 32-bit registers for data [OK]

Common Mistakes:

• Confusing 16-bit or 64-bit as standard size
• Thinking ARM uses 8-bit binary numbers
• Mixing instruction size with data size

2. Which of the following is the correct binary representation format for an ARM instruction?

easy

A. A 16-bit hexadecimal number

B. A 32-bit binary number

C. An 8-bit decimal number

D. A 64-bit binary number

Solution

1. Step 1: Recall ARM instruction size

   ARM instructions are encoded as 32-bit binary numbers to fit the processor's architecture.

2. Step 2: Evaluate options

   The correct format is a 32-bit binary number; the other options use incorrect sizes or formats.

3. Final Answer:

   A 32-bit binary number -> Option B

4. Quick Check:

   ARM instructions = 32-bit binary [OK]

Hint: ARM instructions are always 32-bit binary [OK]

Common Mistakes:

• Confusing binary with hexadecimal
• Choosing 16-bit or 64-bit sizes
• Thinking instructions are decimal numbers

3. Given the 32-bit ARM binary number 00000000000000000000000000001010, what decimal value does it represent?

medium

A. 10

B. 2

C. 8

D. 16

Solution

1. Step 1: Identify the binary number

   The binary number is 32 bits with only the last four bits set: 1010.

2. Step 2: Convert binary 1010 to decimal

   Binary 1010 equals 1*8 + 0*4 + 1*2 + 0*1 = 8 + 0 + 2 + 0 = 10.

3. Final Answer:

   10 -> Option A

4. Quick Check:

   Binary 1010 = Decimal 10 [OK]

Hint: Convert last 4 bits 1010 to decimal 10 [OK]

Common Mistakes:

• Misreading bits and converting 0101 instead
• Confusing binary with hexadecimal
• Ignoring leading zeros

4. An ARM instruction is incorrectly written as 110100101. What is the main issue with this binary representation?

medium

A. It uses hexadecimal instead of binary

B. It contains invalid characters

C. It is too short; ARM instructions require 32 bits

D. It has too many bits; ARM instructions are 8 bits

Solution

1. Step 1: Check length of binary number

   The given binary number has 9 bits, which is shorter than the required 32 bits for ARM instructions.

2. Step 2: Confirm ARM instruction size requirement

   ARM instructions must be exactly 32 bits long to be valid.

3. Final Answer:

   It is too short; ARM instructions require 32 bits -> Option C

4. Quick Check:

   ARM instructions length = 32 bits [OK]

Hint: ARM instructions must be 32 bits long [OK]

Common Mistakes:

• Thinking 9 bits is valid
• Confusing binary with hexadecimal
• Assuming ARM instructions are 8 bits

5. You want to represent the decimal number 255 in ARM's 32-bit binary format. Which binary number correctly represents this value?

hard

A. 00000000000000000000000011111111

B. 11111111000000000000000000000000

C. 00000000000000001111111100000000

D. 11111111111111111111111111111111

Solution

1. Step 1: Convert decimal 255 to binary

   Decimal 255 equals binary 11111111 (8 bits set to 1).

2. Step 2: Format as 32-bit binary

   Place the 8-bit binary 11111111 at the rightmost side and fill the left with zeros to make 32 bits: 00000000000000000000000011111111.

3. Final Answer:

   00000000000000000000000011111111 -> Option A

4. Quick Check:

   255 decimal = 8 rightmost bits set [OK]

Hint: Fill left with zeros, place 255 as 8 ones rightmost [OK]

Common Mistakes:

• Placing ones on left instead of right
• Using all ones (option D) which is 4294967295
• Misaligning bits in the middle