Digit Manipulation

Digit Manipulation
A Programming Pattern

Prof. David Bernstein
James Madison University

Computer Science Department

bernstdh@jmu.edu

Motivation

Recall:
- An int value is "atomic" (i.e., it does not have any constituent parts)
The Issue:
- In many applications we need to manipulate the digits in the int value
An Example:
- Credit cards in which all account numbers are nine digits long and: they never start with a 0, the left-most three digits represent the issuing bank, and the right-most digit indicates the type of account (e.g., debit, credit, crypto currency)

Going Further

: Binary Numbers

Recall:
- int values are represented internally in binary (i.e., base 2)
An Implication:
- Many programming languages allow you to manipulate the individual digits (i.e., bits) of the binary representation
Common Bitwise Binary Operators:
- Shift Left: <<
- Shift Right: >>
- Bitwise And: &
- Bitwise Or: |

Review

Decimal Representation of an Integer

Thinking About the Problem

Thinking About the Problem (cont.)

Addition and/or Multiplication:
- Just make the number larger
Subtraction:
- Might work but doesn't get you very far (e.g., to get the right-most digit from 7198 you'd need to subtract 7190 which requires knowledge of the three left-most digits)
What's Left?
- Integer Division
- The Remainder After Integer Division

The Pattern

Drop the Right-Most n Digits:
- Use integer division (i.e., /)
- Use a right-side operand of \(10^n\)
Extract the Right-Most n Digits:
- Use the remainder after division (i.e., %)
- Use a right-side operand of \(10^n\)

The Pattern (cont.)

Extract the Left-Most n Digits:
- Use integer division (i.e., /)
- Use a right-side operand of \(10^{N-n}\)
Drop the Left-Most n Digits:
- Use the remainder after division (i.e., %)
- Use a right-side operand of \(10^{N-n}\)

Examples

The Setting:
- The account number is 412831758
- The right-most digit is the card type
- The issuing bank is the left-most three digits
- The account holder is identified by the remaining digits
Getting the Card Type:
- \(n = 1\) and \(10^1 = 10\)
- So the card type is given by: 412831758 % 10

Examples (cont.)

The Setting:
- The account number is 412831758
- The right-most digit is the card type
- The issuing bank is the left-most three digits
- The account holder is identified by the remaining digits
Getting the Bank Number:
- \(N - n = 9 - 3 = 6\) and \(10^6 = 1000000\)
- So the bank number is given by: 412831758 / 1000000

Examples (cont.)

The Setting:
- The account number is 412831758
- The right-most digit is the card type
- The issuing bank is the left-most three digits
- The account holder is identified by the remaining digits
Getting the Account Holder:
- First, drop the left-most three digits (so find the remainder after dividing by \(10^6\))
- Then, drop the right-most digit (so divide by \(10^1\))
- So the holder is given by: (412831758 % 1000000) / 10

A Warning

Be Careful:
- When using this pattern repeatedly, the order matters
Example:
- Try performing the operations for finding the account holder in the other order