Question

What value will be assigned to result after the following statement executes? result \(=9 \quad\) \& 2

Short answer

Answer: The value assigned to 'result' is 0.

Step-by-step solution

Understand the bitwise AND operator

The bitwise AND operator (&) compares each bit of the first operand to the corresponding bit of the second operand. If both bits are 1, the corresponding result bit is set to 1. Otherwise, the corresponding result bit is set to 0.

Convert the numbers to binary

We need to convert the two given numbers (9 and 2) into binary format: - 9 in binary: 1001 - 2 in binary: 0010

Perform the bitwise AND operation

Now that we have the binary representation of the numbers, let's perform the bitwise AND operation: 1001 (9) & 0010 (2) _____ 0000 (0)

Convert the binary result back to decimal

The binary result after the bitwise AND operation is 0000. Now we need to convert it back to its decimal representation: - 0000 in decimal: 0

Write the final answer

According to the calculation, the value assigned to 'result' after the given statement executes is 0.

Key concepts

Binary Number System

The binary number system is the backbone of modern computers and digital systems. Unlike the decimal system that uses base 10, the binary system operates on base 2, which only employs two symbols: 0 and 1. Each digit within a binary number is referred to as a 'bit', short for binary digit.

For instance, the binary number 1001 consists of four bits. The rightmost bit is the least significant bit (LSB), and the leftmost bit is the most significant bit (MSB). When calculating with binary numbers, each position represents a power of 2, starting at 0 from the LSB. The value of 1001 in binary translates to \(2^3 + 2^0 = 8 + 1 = 9\) in decimal. Understanding binary is essential for working with bitwise operations, as these operations directly manipulate bits in numbers.

Bitwise Operations in Python

Bitwise operations in Python allow for powerful manipulation of binary digits in numbers. Among these operations, the bitwise AND operator \( \& \) is particularly useful. It takes two numbers, converts them to binary, and then performs a comparison of corresponding bits from both numbers.

If both bits are 1, the resulting bit is set to 1. Otherwise, the result is 0. This can be visualized as follows:

• 1 \( \& \) 1 = 1 (since both are 1)
• 1 \( \& \) 0 = 0 (since one is 0)
• 0 \( \& \) 1 = 0 (since one is 0)
• 0 \( \& \) 0 = 0 (since both are 0)

In Python, this operation is used frequently for tasks such as setting, clearing, and toggling specific bits within a number, making it a staple in low-level programming tasks.

Decimal to Binary Conversion

Converting numbers from decimal to binary is a fundamental process when performing bitwise operations. The conversion involves dividing the decimal number by 2 and tracking the remainder. The process is repeated with the quotient until it is 0. The binary number is then read from the last remainder to the first.

For example, to convert the decimal number 9 to binary, divide by 2 and record the remainder:

• 9 / 2 = 4 remainder 1 (LSB)
• 4 / 2 = 2 remainder 0
• 2 / 2 = 1 remainder 0
• 1 / 2 = 0 remainder 1 (MSB)

Reading the remainders from bottom to top gives the binary number 1001. This method ensures that anyone can easily convert decimal numbers to binary to perform bitwise operations or understand binary systems in computing.