Bash + netcat + ss + …, 65 characters

nc -lp$1 -c"ss src :$1|sed -z 's/.* \b//;y/.:/+#/'|bc"
exec $0 $1

Not a serious solution, was just curious about this possibility.

Sample run:

(terminal 1)

bash-4.3$ ./ip-reduce.sh 8080

(terminal 2)

bash-4.3$ nc localhost 8080
128

bash-4.3$ telnet localhost 8080
Trying 127.0.0.1...
Connected to localhost.
Escape character is '^]'.
128
Connection closed by foreign host.

On Ubuntu you can get nc from netcat-traditional (no, netcat-openbsd is not good) and ss from iproute2.

C#, 284 bytes

class A{static void Main(string[]a){var b=new System.Net.Sockets.TcpListener(int.Parse(a[0]));b.Start(9);for(;;){var c=b.AcceptTcpClient();var d=c.Client.LocalEndPoint.Serialize();var e=new System.IO.StreamWriter(c.GetStream());e.WriteLine(d[4]+d[5]+d[6]+d[7]);e.Flush();c.Close();}}}

Classic example of a basic C# TCP server. Don't run this for too many clients, as it leaks memory (I think). Testing:

Terminal 1:

$ ./Q76379.exe 1029

Terminal 2:

$ telnet localhost 1029
Trying 127.0.0.1...
Connected to localhost.
Escape character is '^]'.
128
Connection closed by foreign host.

Firefox:

Ruby 2.3, 122 105 92 76+7 = 83 bytes

IPV4 only. Port number is first argument.

Golfed

Socket.tcp_server_loop$*[0]{|c,a|c.puts eval a.ip_address.tr'.',?+;c.close}

Ungolfed

require 'socket'

port = ARGV[0]
Socket.tcp_server_loop(port) do |client, addrinfo|
  ipv4_addr_str = addrinfo.ip_address
  sum = eval ipv4_addr_str.tr('.', '+')
  client.puts(sum)
  client.close
end

Output

$ ruby -rsocket server 1234 &
$ nc localhost 1234 -4
128

Python 3, 170 166 147 bytes

from socket import*
s=socket()
s.bind(("",int(input())))
s.listen()
while 1:
 c,a=s.accept()
 c.send(b"%d\n"%eval(a[0].replace(".","+"))),c.close()

Takes port on stdin, IPv4 only. Works on GNU/Linux (and, I assume, most other unices), which automatically expands "" to "0.0.0.0", not sure about Windows though.

PowerShell v2+, 303 268 bytes

($l=new-object Net.Sockets.TcpListener (New-Object Net.IPEndPoint([net.ipaddress]::Any,$args[0]))).Start()
($w=new-object IO.StreamWriter(($c=$l.AcceptTcpClient()).GetStream())).Write((([Net.IPEndPoint]$c.Client.RemoteEndPoint).Address-replace"\.",'+'|iex))
$w.Flush()

_{Saved 35 bytes thanks to Matt}

Leaks memory and system handles like crazy, but we don't care about that, right? :D

Really similar to the C# answer, since it's .NET underlying both. We save a few bytes here over the C# answer by being able to leverage the returning functionality of PowerShell (surrounding our declaration/assignment in parens, and then immediately calling the . methods), but we lose an awful lot by needing to formulate the summation.

The only way (that I've found so far) to get the remote IP address is via the .RemoteEndPoint property, so there's a bunch of string manipulation to get just the IP portion, then -replace the literal periods with plus signs, then pipe it to Invoke-Expression (similar to eval).

If I can figure out some alternate way to get the client's IP address, I should be able to shave a lot of bytes, and maybe even beat the C# answer. But, I'm not hopeful.

Groovy 133, 125, 93, 89

new ServerSocket(args[0]as int).accept{it<<(it.inetAddress.address as int[]).sum()+"\n"}

IPv4 only, probably.

Ungolfed:

new ServerSocket(args[0]as int).accept{
    it << (it.inetAddress.address as int[]).sum()+"\n"
}

Testing:

$ telnet localhost 9000
Trying 127.0.0.1...
Connected to localhost.
Escape character is '^]'.
128
Connection closed by foreign host.

LiveScript, 107 bytes

(require 'http')createServer(->&1.end((.reduce (+))<|it.connection.remoteAddress/'.'))listen process.argv.0

q, 88 bytes

system raze"p ",1_.z.x;.z.pg:{(string sum"i"$0x0 vs .z.a),"\n"};.z.ph:{.h.hy[`;.z.pg[]]}

• system raze"p ",1_.z.x: Takes the second command-line argument (the first "-" is for telling q not to interpret N as a script/file) and opens a port ("p ") with it.
  • Note: Calling q -p N sets the port as N automatically, but since the question seems to suggest that N should be an argument to the program rather than the executable itself, I've gone the longer way.
• Inside the .z.pg function that handles incoming requests, .z.a holds the IP address as a 32-bit integer.
  • "i"$0x0 vs splits it into its integer 'constituents', and sum does the summation.
  • Last, string the numeric result and append "\n" to it to return to the client.
• .z.ph is another function for HTTP GET requests, with extra handling to convert the string output into a valid HTTP response.

Demo - Server:

c:\q\w32>q - 1234
KDB+ 3.3 2015.11.03 Copyright (C) 1993-2015 Kx Systems
w32/ 4()core ... NONEXPIRE

Welcome to kdb+ 32bit edition
q)system raze"p ",1_.z.x;.z.pg:{(string sum"i"$0x0 vs .z.a),"\n"};.z.ph:{.h.hy[`;.z.pg[]]}
q)

Demo - Client (from another q session running on 127.0.0.1):

q)(hopen `::1234)""
"128\n"

Demo - Client (from curl):

$ curl localhost:1234
128

$

Java, 371 368 350 344 333 bytes

Golfed

import java.io.*;import java.net.*;interface A{public static void main(String[]n)throws Exception{ServerSocket s=new ServerSocket(Integer.parseInt(n[0]));for(;;){Socket a=s.accept();byte[]c=a.getInetAddress().getAddress();new DataOutputStream(a.getOutputStream()).writeBytes(Integer.toString(c[0]+c[1]+c[2]+c[3])+"\n");a.close();}}}

Ungolfed

import java.io.*;
import java.net.*;

interface A {
    public static void main(String[] n) throws Exception {
        ServerSocket s = new ServerSocket(Integer.parseInt(n[0]));
        for (;;) {
            Socket a = s.accept();
            byte[] c = a.getInetAddress().getAddress();
            new DataOutputStream(a.getOutputStream()).writeBytes(Integer.toString(c[0] + c[1] + c[2] + c[3]) + "\n");
            a.close();
        }
    }
}

Output

mallard@steamroller:~$ telnet localhost 8888
Trying 127.0.0.1...
Connected to localhost.
Escape character is '^]'.
128
Connection closed by foreign host.

NodeJS, 146 bytes

require('http').createServer(function(q,s){s.end(eval(q.socket.remoteAddress.replace(/^.*:/,'').replace(/\./g,'+'))+'\n')}).listen(process.argv[2])

I finally get to post a NodeJS answer! IPv4 only right now.

Sample execution: node script.js 1024. From another terminal:

$ curl 127.0.0.1:1024
128

Tcl, 93

proc s {c a p} {puts $c [expr [string map {. +} $a]]
close $c}
socket -server s $argv
vwait f

Fairly self-explanatory. socket -server s $argv creates a listening socket on the port specified in the arguments. Every time a new connection arrives, the proc s is called, with channel, source-address and source-port as parameters. string map substitutes . for + in the source address, and expr arithmetically evaluates the result, which is then puts back to the connection channel c. vwait runs an event loop to catch the incoming connection events.

Perl, 141 + 1 = 142 bytes

Golfed

$s=new IO::Socket::INET(LocalPort=><>,Listen=>5,Reuse=>1);while(1){$c=$s->accept();$_=$c->peerhost();y/./+/;$c->send(eval.$/);shutdown($c,1)}

Ungolfed

# listen on tcp port obtained from stdin
$s=new IO::Socket::INET(LocalPort=> <>,
                        Listen   => 5,
                        Reuse    => 1);

while(1) {
    # accept connection
    $c=$s->accept();

    # get the ip address
    $_=$c->peerhost();

    # replace dots with plus
    y/./+/;

    # send the evaluated version back, with a newline
    $c->send(eval . $/);

    # close
    shutdown($c,1);
}

Example

$ echo 7777 | perl -MIO::Socket::INET -e '$s=new IO::Socket::INET(LocalPort=><>,Listen=>5,Reuse=>1);while(1){$c=$s->accept();$_=$c->peerhost();y/./+/;$c->send(eval.$/);shutdown($c,1)}'

$ telnet 127.0.0.1 7777
Trying 127.0.0.1...
Connected to 127.0.0.1.
Escape character is '^]'.
128
Connection closed by foreign host.
$