Add the binary numbers 10₂ and 11₂ and express the sum in binary.
Computer Science
Digital Computer Electronics
Difficulty: Easy
Choose an option
-
A100₂
-
B101₂
-
C111₂
-
D110₂
-
ENone of the above
Answer
Correct Answer: 101₂
Explanation
Introduction / Context:Binary addition is fundamental to arithmetic logic units (ALUs) and digital circuits. This item reinforces carry handling when summing two small binary numbers.
Given Data / Assumptions:
- Operands: 10₂ and 11₂.
- No signed interpretation; simple unsigned addition.
Concept / Approach:
- Binary addition rules: 0+0=0, 0+1=1, 1+0=1, 1+1=0 with carry 1.
- Align bits from least significant to most significant and add with carries.
Step-by-Step Solution:
Write vertically: 10₂ + 11₂.LSB column: 0 + 1 = 1 (carry 0).Next column: 1 + 1 = 0 with carry 1.Append carry to the left: result = 101₂.Verification / Alternative check:
Convert to decimal: 10₂=2, 11₂=3; 2+3=5; 5 in binary is 101₂.Why Other Options Are Wrong:
- 100₂: Equals 4, not 5.
- 111₂: Equals 7, not 5.
- 110₂: Equals 6, not 5.
- None of the above: Incorrect because 101₂ is correct.
Common Pitfalls:
- Dropping the final carry when 1+1 occurs.
- Misaligning bit columns when adding.
Final Answer:
101₂