Direct Inward Dialing Number (Also known as DID or DDI)

Simple Definition: DID equals a Telephone Number or Telephone Extension on a PBX reachable directly from outside the PBX by Dialing the DID.
a DID is owned by the Carrier who has Facilities within the Local Calling Area, and can be leased or assigned to any other Client including a VoIP carrier
who is seen simply as the Client or Reseller. Once a DID is assigned to a Client, that client owns it for as long as they pay for it, and they may port or transfer this
to any other Carrier which has Facilities. Since most VoIP carriers support TDM to SIP today, so are many CLECs converting to allowing TDM to SIP interconnections.

For Example: Take a CLEC (US Only Competitive Local Exchange Carrier) like HyperCube Telecom HyperCube, which has TDM Facilities within 20+ USA only States and has been assigned thousands of blocks of Telephone Numbers by NANPA Neustar. HyperCube takes these TNs or DIDs, and allows a VoIP carrier like Keku keku to then subscribe them to a calling card or client. Typically, the Call originates over the PSTN>> is sent to HyperCube's Switch then routes over to HyperCube's Sonus Network which is then sent to the VoIP carriers IP gateway using Public or Private internet connections.. which then terminates to a SIP Device or App which receives the call and routes it on to some other destinations.

DID (DDI) Background
Most businesses have several incoming telephone numbers used for specific purposes. For example customer service, sales, etc. Some have an individual telephone number for each user in the system. In a home setting on the other hand, each telephone number comes in on a different pair of wires typically. This is not practical in a business enviroment that has many telephone numbers.

Why was DID actually Created?
So DID ("direct inward dialing") was invented as a way to re-use a limited number of physical phone lines to handle calls to different published numbers. In a business with DID, the phone company uses DID signalling to identify the number they are about to connect to the business's PBX. Historically, this was done by pulsing the last 3 or 4 digits of the number being dialed before connecting the number. The PBX would use these DID digits to switch the call to the right recipient.

In modern PBX's, typically, digital methods (example: PRI) are used to do the same thing, ie. supply the "called party" information. But many business's still have old PBX's which use the analog signalling I mentioned before. The type of telephone lines used for analog DID are different than regular home telephone lines. Usually, battery voltage is supplied by the business PBX instead of the telco. Also, the telco signals a new call by bridging the line instead of by ringing the line. The receiving PBX signals back that it's ready to take the call by momentarily reversing polarity of the voltage on the line (this is called "winking" the line)

Old Fashion Way: (PSTN WORLD)
Direct Inward Dialing is used when your PBX telco connection allows direct dialling to extensions within a PBX, using physical lines (or channels on a PRI) on a shared basis. DID service consists of identifying the "called party" by using DTMF or by digital means, before connecting each call. The service can be sent over an E&M Wink T-1 as DTMF and also as D-Channel information on a PRI.

On a PRI connection, the telco can send only the digits that differ between the group number and the extension (often four digits) or the whole number - it depends on the connection to the telco.

DID (DDI) in the new VOIP World

Let's say you buy a phone line from Vonage or some other phone service provider who offers phone service over broadband. The number that they provide to you, in technical terms is a DID number. This is the number that they have assigned to you to connect you to the old PSTN Networks around the world. ...