Answer to Question #272402 in Discrete Mathematics for Amu Raj

Question

1. Discuss ways in which the current telephone numbering plan can be extended to accommodate the rapid demand for more telephone numbers. (See if you can find some of the proposals coming from the telecommunications industry.) For each new numbering plan you discuss, show how to find the number of different telephone numbers it supports.

Answer 1

Telephone numbering system has some design strategies so that no

one get the same number means unique number.This design strategies

varies from country to country. For example :in India:

Landline format =area code+number

Mobile number = country code+10 digit number

As we know with the increase in technology, demands are also

increases which need an extending plan:

1)Relocating the existing numbers for paging services and

re-allocating some of the numbers in the “7(0-3)X” levels for

mobile services.

for X = n digits can support $4\cdot10^n$ numbers

2) Re-allocating numbers in the “4X” level for mobile services,

which will be able to release 5.6 million numbers to meet the

demand

for X = n digits can support $10^n$ numbers

3) Re-allocating vacant numbers in the “8(1-3)X” levels for

mobile services

for X = n digits can support $3\cdot10^n$ numbers

4) Raising the threshold of utilisation rate for allocation of

additional numbers to network operators, which will be able to

release 2.42 million numbers to meet the demand

5) Releasing most of the Special Number Blockss1for normal

allocation, which will be able to release a maximum of 3.52 million

numbers to meet the demand