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 $1$s, and the remaining $32 - N$ bits will be $0$s.
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:
$$ \underbrace{11111111}_{8 \text{ bits}} \underbrace{11111111}_{8 \text{ bits}} \underbrace{11111111}_{8 \text{ bits}} \underbrace{11000000}_{8 \text{ bits}} $$
(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:
• $11111111_2 = 255_{10}$
• $11111111_2 = 255_{10}$
• $11111111_2 = 255_{10}$
• $11000000_2 = (1 \times 128) + (1 \times 64) + (0 \times 32) + (0 \times 16) + (0 \times 8) + (0 \times 4) + (0 \times 2) + (0 \times 1) = 128 + 64 = 192_{10}$
The decimal subnet mask for $/26$ is $\boxed{255.255.255.192}$.
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How do you calculate for the decimal subnet
|Mathematics
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:
8bits111111118bits111111118bits111111118bits11000000
(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:
• 111111112=25510
• 111111112=25510
• 111111112=25510
• 110000002=(1×128)+(1×64)+(0×32)+(0×16)+(0×8)+(0×4)+(0×2)+(0×1)=128+64=19210
The decimal subnet mask for /26 is 255.255.255.192.
That's 2 down. 3 left today — send the next one.
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