Binary number system in Intro to Computing - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ trace

intermediate

Trace the binary addition

What is the result of adding the binary numbers 1011 and 1101? Show the final binary sum.

A 10110

B 11000

C 10000

D 11110

💡 Hint

Add each bit from right to left, carrying over when sum exceeds 1.

Adding 1011 (11 decimal) and 1101 (13 decimal) in binary:

• 1 + 1 = 10 (write 0, carry 1)
• 1 + 0 + carry 1 = 10 (write 0, carry 1)
• 0 + 1 + carry 1 = 10 (write 0, carry 1)
• 1 + 1 + carry 1 = 11 (write 1, carry 1)
• Carry 1 is written as the leftmost bit

Final sum: 11000 (24 decimal).

🧠 Conceptual

intermediate

Understanding binary place values

Which decimal number does the binary number 100101 represent?

A 41

B 29

C 37

D 45

💡 Hint

Calculate the sum of powers of 2 where bits are 1.

Binary 100101 means:

• 1 × 2⁵ = 32
• 0 × 2⁴ = 0
• 0 × 2³ = 0
• 1 × 2² = 4
• 0 × 2¹ = 0
• 1 × 2⁰ = 1

Sum = 32 + 4 + 1 = 37 decimal.

❓ Comparison

advanced

Compare binary and decimal representations

Which of the following binary numbers is greater than decimal 20 but less than decimal 30?

A 11001

B 11100

C 10101

D 10011

💡 Hint

Convert each binary to decimal and check the range.

Convert each binary to decimal:

• 10101 = 21
• 11100 = 28
• 11001 = 25
• 10011 = 19

Numbers greater than 20 and less than 30 are 21, 25, and 28. Among options, 21 (10101), 25 (11001), and 28 (11100) fit the condition.

❓ identification

advanced

Identify the error in binary to decimal conversion

A student converts binary 1110 to decimal and writes the result as 14. What is the mistake in their conversion?

A They correctly converted; 1110 is 14 decimal.

B They forgot to multiply the leftmost bit by 8.

C They added the place values incorrectly; 1110 is 15 decimal.

D They reversed the bits; 1110 is 7 decimal.

💡 Hint

Calculate the decimal value of 1110 carefully.

Binary 1110 means:

• 1 × 2³ = 8
• 1 × 2² = 4
• 1 × 2¹ = 2
• 0 × 2⁰ = 0

Sum = 8 + 4 + 2 + 0 = 14 decimal, so the student's conversion is correct.

🚀 Application

expert

Convert and add binary numbers with carry

What is the decimal value of the binary sum of 1111 and 1011? Show the final decimal result.

A 32

B 30

C 28

D 26

💡 Hint

Add the binary numbers bit by bit, then convert the result to decimal.

Adding 1111 (15 decimal) and 1011 (11 decimal) in binary:

• 1 + 1 = 10 (write 0, carry 1)
• 1 + 1 + carry 1 = 11 (write 1, carry 1)
• 1 + 0 + carry 1 = 10 (write 0, carry 1)
• 1 + 1 + carry 1 = 11 (write 1, carry 1)
• Carry 1 is written as the leftmost bit

Final binary sum: 11010

Convert 11010 to decimal: 16 + 8 + 0 + 2 + 0 = 26 decimal.

Correction: The sum binary is 11010 which is 26 decimal, so option D is correct.