Binary representation in ARM in ARM Architecture - Step-by-Step Execution

Concept Flow - Binary representation in ARM

Start with decimal number

↓

Divide number by 2

↓

Record remainder (0 or 1)

↓

Update number = quotient

↓

Is number > 0?

No→Stop

Yes↓

Collect remainders in reverse order

↓

Result: Binary representation

↩Back to Divide

Convert a decimal number to binary by repeatedly dividing by 2 and recording remainders, then reversing them to get the binary form used in ARM.

Execution Sample

ARM Architecture

Decimal: 13
13 / 2 = 6 remainder 1
6 / 2 = 3 remainder 0
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1
Binary = 1101

Shows step-by-step division by 2 to convert decimal 13 to binary 1101.

Analysis Table

Step	Number	Divide by 2	Quotient	Remainder	Binary so far
1	13	13 / 2	6	1	1
2	6	6 / 2	3	0	01
3	3	3 / 2	1	1	101
4	1	1 / 2	0	1	1101
5	0	Stop	-	-	1101

💡 Number reached 0, division stops, binary collected in reverse order then reversed to get final binary.

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
Number	13	6	3	1	0	0
Remainder	-	1	0	1	1	-
Binary (reversed)		1	01	101	1101	1101

Key Insights - 3 Insights

Why do we collect remainders in reverse order?

Because each remainder represents the least significant bit first, so reversing them gives the correct binary from most to least significant bit, as shown in execution_table rows 1-4.

What happens when the number becomes zero?

The division stops because zero means no more bits to process, as shown in execution_table step 5 where number is 0 and process ends.

Why divide by 2 specifically for binary?

Dividing by 2 splits the number into bits of base 2, which is the binary system ARM uses internally, demonstrated in each division step in execution_table.

Visual Quiz - 3 Questions

Look at the execution_table at Step 3, what is the remainder recorded?

A 1

B 0

C 3

D 6

💡 Hint

Check the 'Remainder' column at Step 3 in the execution_table.

At which step does the number become zero, stopping the division?

A Step 4

B Step 5

C Step 2

D Step 1

💡 Hint

Look at the 'Number' column in execution_table to find when it reaches zero.

If the initial number was 8 instead of 13, what would be the first remainder recorded?

A 8

B 1

C 0

D 4

💡 Hint

Recall that dividing an even number by 2 leaves remainder 0, check variable_tracker for remainder patterns.

Concept Snapshot

Binary representation in ARM:
- Convert decimal to binary by dividing by 2 repeatedly.
- Record remainders (0 or 1) each division.
- Stop when number reaches 0.
- Reverse collected remainders for final binary.
- ARM uses this binary internally for data and instructions.

Full Transcript

To represent numbers in ARM, we convert decimal numbers to binary. This is done by dividing the number by 2 repeatedly and recording the remainder each time. The remainder is either 0 or 1, representing bits. We continue until the number becomes zero. The binary number is formed by reversing the order of the remainders collected. For example, decimal 13 converts to binary 1101 by dividing 13 by 2 four times and collecting remainders 1,0,1,1 in reverse order. This binary form is how ARM stores and processes numbers internally.

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