Computer science: reference Theory of Computation $-$ pushdown automata

The first six or eight digits of the credit card represent the Issuer Identification Number $($IIN$),$ also known as the Bank Identification Number $($BIN$).$

American Express cards always begin with the number $3,$ more specifically $34$ or $37.$

Visa cards begin with the number $4.$

Mastercards start with the number $5.$

Discover Cards begin with the number $6.$

Problem: Implementing credit card machine to accept valid BIN digits mentioned above and reject invalid BIN digits $($ie: any credit card start with digits doesn't not match above BIN$)$

implement it with pushdown automata, you should have at least $5$ states in this problem and give at least $3$ of $5$ cases that your "machine" accepts.

Also,

$1-$ Describe the alphabet of this problem.

$2-$ Give a description of the states for this problem..

$3-$ Give a description of the start and accept states for this problem.