Theory:

Step 1: If the given time is \(12\!:\!00\) a.m. (midnight), change \(12\!:\!00\) a.m. as \(00\!:\!00\) hours and proceed further. There is no change up to \(12\!:\!59\) p.m.
 
Step 2: If the given time is \(1\!:\!00\) a. m. to \(12\!:\!59\) p.m., then no time change in \(24\)-hour format. Just write the time as it is in \(4\) digits.
 
Step 3: If the given time is \(1\!:\!00\) p.m. to \(11\!:\!59\) p.m., add \(12\!:\!00\) hours to the given time and write it in \(4\) digits.
Example:
1. Convert \(12\!:\!15\) a.m. to \(24\)-hour format.
 
Solution:
 
By using the above procedure, change \(12\!:\!00\) a.m. as \(00\!:\!00\) hours.
 
Therefore, \(12\!:\!15\) a.m. \(=\) \(00\!:\!15\) hours
 
 
2. Write \(8\!:\!45\) a.m. in \(24\)-hour format.
 
Solution:
 
\(8\!:\!45\) a.m. lies between \(1\!:\!00\) a.m. to \(12\!:\!59\) p.m.
 
By the above procedure, no time change between \(1\!:\!00\) a.m. to \(12\!:\!59\) p.m.
 
Write the time as it is in \(4\) digits.
 
Therefore, \(8\!:\!45\) a.m. \(=\) \(08\!:\!45\) hours.
 
 
3. Convert \(8:45\) p.m. in railway format.
 
Solution:
 
\(8:45\) p.m. lies between \(1:00\) p.m. to \(11:59\) p.m.
 
Add \(12:00\) hours to the given time by the above procedure.
 
8:45+12:00¯20:45¯
 
Therefore, \(8:45\) p.m. \(=\) \(20:45\) hours.
Important!
1. Write hours at the end of the \(24\)-hour time format. Don't write a.m. or p.m. at the end of \(24\)-hour format.
 
2. Minutes will not change in both \(12\)-hour and \(24\)-hour formats.