Question

Given the IP address and subnet mask 214.20.1.15/255.255.255.192 (/26)

Whats the subnet ip range, network ID, broadcast address, and number of available IPs in the subnet

Answer #1

subnet ip range: 214.20.1.1 to 214.20.1.62 network ID: 214.20.1.0 broadcast address: 214.20.1.63 number of available IPs: 62Explanation: ------------- IP Address: 214.20.1.15 ---------------------------------------- Let's first convert this into binary format 214.20.1.15 Let's convert all octets to binary separately Converting 214 to binary Divide 214 successively by 2 until the quotient is 0 > 214/2 = 107, remainder is 0 > 107/2 = 53, remainder is 1 > 53/2 = 26, remainder is 1 > 26/2 = 13, remainder is 0 > 13/2 = 6, remainder is 1 > 6/2 = 3, remainder is 0 > 3/2 = 1, remainder is 1 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 11010110 So, 214 of decimal is 11010110 in binary 214 in binary is 11010110 Converting 20 to binary Divide 20 successively by 2 until the quotient is 0 > 20/2 = 10, remainder is 0 > 10/2 = 5, remainder is 0 > 5/2 = 2, remainder is 1 > 2/2 = 1, remainder is 0 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 10100 So, 20 of decimal is 10100 in binary 20 in binary is 00010100 Converting 1 to binary Divide 1 successively by 2 until the quotient is 0 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 1 So, 1 of decimal is 1 in binary 1 in binary is 00000001 Converting 15 to binary Divide 15 successively by 2 until the quotient is 0 > 15/2 = 7, remainder is 1 > 7/2 = 3, remainder is 1 > 3/2 = 1, remainder is 1 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 1111 So, 15 of decimal is 1111 in binary 15 in binary is 00001111 ================================================================================== || 214.20.1.15 in binary notation is 11010110.00010100.00000001.00001111 || ================================================================================== Subnet address: 255.255.255.192 ---------------------------------------- Let's convert this into binary format 255.255.255.192 Let's convert all octets to binary separately Converting 255 to binary Divide 255 successively by 2 until the quotient is 0 > 255/2 = 127, remainder is 1 > 127/2 = 63, remainder is 1 > 63/2 = 31, remainder is 1 > 31/2 = 15, remainder is 1 > 15/2 = 7, remainder is 1 > 7/2 = 3, remainder is 1 > 3/2 = 1, remainder is 1 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 11111111 So, 255 of decimal is 11111111 in binary 255 in binary is 11111111 Converting 255 to binary Divide 255 successively by 2 until the quotient is 0 > 255/2 = 127, remainder is 1 > 127/2 = 63, remainder is 1 > 63/2 = 31, remainder is 1 > 31/2 = 15, remainder is 1 > 15/2 = 7, remainder is 1 > 7/2 = 3, remainder is 1 > 3/2 = 1, remainder is 1 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 11111111 So, 255 of decimal is 11111111 in binary 255 in binary is 11111111 Converting 255 to binary Divide 255 successively by 2 until the quotient is 0 > 255/2 = 127, remainder is 1 > 127/2 = 63, remainder is 1 > 63/2 = 31, remainder is 1 > 31/2 = 15, remainder is 1 > 15/2 = 7, remainder is 1 > 7/2 = 3, remainder is 1 > 3/2 = 1, remainder is 1 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 11111111 So, 255 of decimal is 11111111 in binary 255 in binary is 11111111 Converting 192 to binary Divide 192 successively by 2 until the quotient is 0 > 192/2 = 96, remainder is 0 > 96/2 = 48, remainder is 0 > 48/2 = 24, remainder is 0 > 24/2 = 12, remainder is 0 > 12/2 = 6, remainder is 0 > 6/2 = 3, remainder is 0 > 3/2 = 1, remainder is 1 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 11000000 So, 192 of decimal is 11000000 in binary 192 in binary is 11000000 ====================================================================================== || 255.255.255.192 in binary notation is 11111111.11111111.11111111.11000000 || ====================================================================================== Remove all dots to form 11111111111111111111111111000000 Remove all 0's from the right side to form 11111111111111111111111111 Number of 1's in this is 26 so, Subnet mask is /26 For Calculating network ID, keep first 26 bits of 11010110.00010100.00000001.00001111 and set all remaining bits to 0. so, network ID in binary is 11010110.00010100.00000001.00000000 11010110.00010100.00000001.00000000: ---------------------------------------- 11010110.00010100.00000001.00000000 Let's convert all octets to decimal separately Converting 11010110 to decimal Converting 11010110 to decimal 11010110 => 1x2^7+1x2^6+0x2^5+1x2^4+0x2^3+1x2^2+1x2^1+0x2^0 => 1x128+1x64+0x32+1x16+0x8+1x4+1x2+0x1 => 128+64+0+16+0+4+2+0 => 214 11010110 in decimal is 214 Converting 00010100 to decimal Converting 00010100 to decimal 00010100 => 0x2^7+0x2^6+0x2^5+1x2^4+0x2^3+1x2^2+0x2^1+0x2^0 => 0x128+0x64+0x32+1x16+0x8+1x4+0x2+0x1 => 0+0+0+16+0+4+0+0 => 20 00010100 in decimal is 20 Converting 00000001 to decimal Converting 00000001 to decimal 00000001 => 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+1x2^0 => 0x128+0x64+0x32+0x16+0x8+0x4+0x2+1x1 => 0+0+0+0+0+0+0+1 => 1 00000001 in decimal is 1 Converting 00000000 to decimal Converting 00000000 to decimal 00000000 => 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0 => 0x128+0x64+0x32+0x16+0x8+0x4+0x2+0x1 => 0+0+0+0+0+0+0+0 => 0 00000000 in decimal is 0 ================================================================================== || 11010110.00010100.00000001.00000000 in decimal notation is 214.20.1.0 || ================================================================================== ========================================= || So, Network ID is 214.20.1.0 || ========================================= For Calculating broadcast ID, keep first 26 bits of 11010110.00010100.00000001.00001111 and set all remaining bits to 1. so, broadcast ID in binary is 11010110.00010100.00000001.00111111 11010110.00010100.00000001.00111111: ---------------------------------------- 11010110.00010100.00000001.00111111 Let's convert all octets to decimal separately Converting 11010110 to decimal Converting 11010110 to decimal 11010110 => 1x2^7+1x2^6+0x2^5+1x2^4+0x2^3+1x2^2+1x2^1+0x2^0 => 1x128+1x64+0x32+1x16+0x8+1x4+1x2+0x1 => 128+64+0+16+0+4+2+0 => 214 11010110 in decimal is 214 Converting 00010100 to decimal Converting 00010100 to decimal 00010100 => 0x2^7+0x2^6+0x2^5+1x2^4+0x2^3+1x2^2+0x2^1+0x2^0 => 0x128+0x64+0x32+1x16+0x8+1x4+0x2+0x1 => 0+0+0+16+0+4+0+0 => 20 00010100 in decimal is 20 Converting 00000001 to decimal Converting 00000001 to decimal 00000001 => 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+1x2^0 => 0x128+0x64+0x32+0x16+0x8+0x4+0x2+1x1 => 0+0+0+0+0+0+0+1 => 1 00000001 in decimal is 1 Converting 00111111 to decimal Converting 00111111 to decimal 00111111 => 0x2^7+0x2^6+1x2^5+1x2^4+1x2^3+1x2^2+1x2^1+1x2^0 => 0x128+0x64+1x32+1x16+1x8+1x4+1x2+1x1 => 0+0+32+16+8+4+2+1 => 63 00111111 in decimal is 63 =================================================================================== || 11010110.00010100.00000001.00111111 in decimal notation is 214.20.1.63 || =================================================================================== ============================================ || So, broadcast ID is 214.20.1.63 || ============================================ For Calculating first valid address in subnet, add 1 to the network address. Network Address is 214.20.1.0 ============================================================ || So, first valid address in subnet is 214.20.1.1 || ============================================================ For Calculating last valid address in subnet, remove 1 from the broadcast address. Broadcast Address is 214.20.1.63 ============================================================ || So, last valid address in subnet is 214.20.1.62 || ============================================================ Number of valid hosts in the network > 2^(32 - number of 1's in subnet) - 2 > 2^(32 - 26) - 2 > 2^(6) - 2 > 64 - 2 > 62 ========================================================== || So, number of valid hosts in the subnet is 62 || ==========================================================

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