Question

Match the solution with the problem. A. 10001100 B. 10011110 C. 1101010 D. 1100000 E. 1010001 F. 1111000 \(1010110-101\) (binary subtraction)

Short answer

There is no matching choice; result is 1001001 not in options.

Step-by-step solution

Align the Numbers

First, write down the number 1010110 and align the number 101 directly below it starting from the rightmost digit, ensuring that the digits are aligned by their place values.

Perform Binary Subtraction

Subtract each pair of digits from the right to the left, borrowing as necessary. The operation works as follows: 1. From the rightmost bit: 0 (from 6th position) - 1 = 1 after borrowing. 2. 0 (5th position) - 0 = 0, no borrowing needed. 3. 1 (4th position) - 1 = 0. 4. 0 (3rd position) - 0 = 0. 5. 1 (2nd position) - nothing = 1. 6. 0 (1st position) - nothing = 0. 7. 1 (0th position) - nothing = 1. The result will be 1001001.

Match the Result with Given Options

Compare 1001001 with the given options. You will find that none of the provided options match the result 1001001 directly.

Key concepts

Binary Subtraction

Binary subtraction is a fundamental operation in binary arithmetic. It's akin to the subtraction process you may already know from decimal numbers, but it has its unique features due to the base-2 number system.
In binary, each digit can only be 0 or 1. When performing binary subtraction, you align the numbers by their least significant bit or rightmost digit. You subtract directly, but when a larger digit has to be subtracted from a smaller one, you need to "borrow" from the next left bit.
Borrowing in binary works similarly to decimal systems, but since binary has only two digits, the borrowed value is 2 in decimal terms. Thus, if you need to subtract 1 from 0, you must first borrow a 1 from the next higher bit position. This makes the 0 into a 2 (in binary), allowing you to complete the subtraction with a result of 1 below it. This borrowing process is crucial for problem-solving in binary and helps build a robust understanding of how computer operations work.

Computer Science Education

Understanding binary arithmetic operations is essential for grasping the fundamentals of computer science education. Computers operate using binary logic, and these arithmetic processes form the backbone of many computational tasks.
Students often begin learning binary systems in introductory computer science courses, which sets the foundation for more advanced topics such as computer architecture and digital electronics. Mastering binary operations like addition, subtraction, multiplication, and division is crucial for later understanding how algorithms and programs are constructed and executed within a computer system.
Moreover, binary arithmetic enhances logical thinking skills, providing students with new tools for problem-solving that are applicable in wider technological contexts. Educators often focus on practical exercises like binary subtraction to demonstrate the real-world applications of these abstract concepts, making computer science education both engaging and meaningful.

Problem-solving in Binary

Problem-solving in binary requires an understanding of both the binary number system and logical methodologies to carry out various arithmetic operations. It is a skill that blends mathematical techniques with critical thinking.
To solve problems in binary effectively, follow a systematic approach:

• Identify the problem and the binary numbers involved.
• Align the numbers by their rightmost digit for accuracy in operations.
• Perform the necessary arithmetic, such as addition or subtraction, carefully considering borrowing or carrying when needed.
• Verify your result by re-calculating or checking against given options if it's a multiple-choice format.

Developing fluency in binary problem-solving enhances your ability to tackle complex technical challenges and supports a deeper understanding of digital systems. As you become comfortable with these operations, more advanced concepts in computer science and technology become accessible, empowering you to build upon this foundation for innovative solutions and applications.