This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To calculate a decimal subnet mask from a CIDR prefix length (e.g., /24), follow these steps: Step 1: Understand the prefix length. The prefix length (e.g., N in /N) indicates the number of network bits from the left in a 32-bit IPv4 address. The remaining 32 - N bits are host bits. Step 2: Write the subnet mask in binary. Create a 32-bit binary number. The first N bits will be 1s, and the remaining 32 - N bits will be 0s. Step 3: Divide the binary mask into four 8-bit octets. Group the 32 binary bits into four sets of 8 bits. Step 4: Convert each binary octet to its decimal equivalent. Convert each 8-bit binary number into its decimal value. These four decimal values, separated by dots, form the dotted-decimal subnet mask. Example: Calculate the decimal subnet mask for /26. Step 1: The prefix length is N=26. This means there are 26 network bits and 32 - 26 = 6 host bits. Step 2: Write the 32-bit binary mask: 11111111_8 bits 11111111_8 bits 11111111_8 bits 11000000_8 bits (26 ones followed by 6 zeros) Step 3: Divide into four octets: • First octet: 11111111 • Second octet: 11111111 • Third octet: 11111111 • Fourth octet: 11000000 Step 4: Convert each octet to decimal: • 11111111_2 = 255_10 • 11111111_2 = 255_10 • 11111111_2 = 255_10 • 11000000_2 = (1 × 128) + (1 × 64) + (0 × 32) + (0 × 16) + (0 × 8) + (0 × 4) + (0 × 2) + (0 × 1) = 128 + 64 = 192_10 The decimal subnet mask for /26 is 255.255.255.192. That's 2 down. 3 left today — send the next one.