Convert the 32 bit binary IPv4 address 10100010111101011001110110001011 (base 2) to its dotted decimal form.

Introduction / Context:
Understanding how to convert between binary and dotted decimal IPv4 addresses is an essential skill for network engineers. IP addresses are stored and processed in binary by devices, but humans typically read and configure them in dotted decimal format. This question tests your ability to take a 32 bit binary string and convert it into its equivalent dotted decimal address.

Given Data / Assumptions:

The binary address is 10100010111101011001110110001011 in base 2.
The address is an IPv4 address, so it must be split into four 8 bit octets.
We must convert each octet from binary to decimal and join them with dots.

Concept / Approach:
An IPv4 address consists of 32 bits grouped into four octets of 8 bits each. To convert from binary to dotted decimal, split the 32 bit string into four 8 bit segments, convert each segment from base 2 to base 10, and then write the result as decimal numbers separated by dots. For each octet, you can use positional values of 128, 64, 32, 16, 8, 4, 2, and 1 to compute the decimal value by summing the weights where the bit is 1.

Step-by-Step Solution:
Step 1: Split the 32 bit binary string into four octets: 10100010, 11110101, 10011101, and 10001011.Step 2: Convert the first octet 10100010 to decimal: 128 + 32 + 2 = 162.Step 3: Convert the second octet 11110101 to decimal: 128 + 64 + 32 + 16 + 4 + 1 = 245.Step 4: Convert the third octet 10011101 to decimal: 128 + 16 + 8 + 4 + 1 = 157.Step 5: Convert the fourth octet 10001011 to decimal: 128 + 8 + 2 + 1 = 139.Step 6: Combine the four decimal values into dotted decimal form: 162.245.157.139.

Verification / Alternative check:
An alternative check is to use smaller groups and verify each octet separately. You can also quickly approximate: the first bit of each octet represents 128, so any octet beginning with 1 must be at least 128, which helps reject options where octets have impossible ranges. All four octets in this example begin with 1, so each decimal value must be 128 or higher, matching 162, 245, 157, and 139. This cross check confirms the detailed conversion.

Why Other Options Are Wrong:
Option B is wrong because the first octet 161 does not match the correct conversion of 10100010, which is 162, not 161.
Option C is wrong because it changes the second octet from 245 to 244, which does not correspond to 11110101.
Option D is wrong because it changes the third octet from 157 to 158, again breaking the exact binary to decimal mapping.

Common Pitfalls:
Common mistakes include mis grouping bits into incorrect octets, forgetting that IPv4 requires exactly 8 bits per octet, and making arithmetic errors when adding the positional values. Some learners also accidentally convert from left to right without using positional weights correctly. To avoid errors, always write the bit positions and their weights, then sum only where the bit is 1.

Final Answer:
162.245.157.139