Question

What subnet mask would you use for the 178.32.0.0 network, such that you can get 50 subnets and 1000 hosts per subnet?

Please show work.

Answer 1

255.255.252.0 or /22

Explanation:
-------------
default subnet mask is /16 or 255.255.0.0
number of subnets = 50
number of additional bits for subnet mask = log2(50) = 5.64 => 6 bits
total number of bits in subnet mask = 16+6 = 22

So, subnet mask in binary is 11111111.11111111.11111100.00000000
Now, let's convert this to decimal
11111111.11111111.11111100.00000000
Let's convert all octets to decimal separately
Converting 11111111 to decimal
Converting 11111111 to decimal
11111111
=> 1x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+1x64+1x32+1x16+1x8+1x4+1x2+1x1
=> 128+64+32+16+8+4+2+1
=> 255
11111111 in decimal is 255

Converting 11111111 to decimal
Converting 11111111 to decimal
11111111
=> 1x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+1x64+1x32+1x16+1x8+1x4+1x2+1x1
=> 128+64+32+16+8+4+2+1
=> 255
11111111 in decimal is 255

Converting 11111100 to decimal
Converting 11111100 to decimal
11111100
=> 1x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+0x2^1+0x2^0
=> 1x128+1x64+1x32+1x16+1x8+1x4+0x2+0x1
=> 128+64+32+16+8+4+0+0
=> 252
11111100 in decimal is 252

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

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||    11111111.11111111.11111100.00000000 in decimal notation is 255.255.252.0    ||
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So, subnet mask in decimal is 255.255.252.0