Char Arithmetic and Modular Shift

Java chars are stored as integer codes (ASCII / Unicode). 'A' is 65; 'B' is 66; 'a' is 97. This means you can do arithmetic on them: (char)(c + 1) produces the next character.

The Caesar cipher shifts every letter by a fixed amount, wrapping around the alphabet. The wrap is handled with % on the letter index (0-25).

On the AP exam, char arithmetic appears in shift-cipher FRQs and char-to-index conversion problems.

Basic arithmetic

char c = 'A';
char next = (char)(c + 1);   // 'B'
int diff = 'D' - 'A';        // 3

Adding a number to a char produces an int; cast back to char to get a character.

Caesar shift with wrap

public char shift(char c, int amount) {
    if (c >= 'a' && c <= 'z') {
        int index = c - 'a';                       // 0-25
        int shifted = (index + amount) % 26;       // wrap
        return (char)('a' + shifted);              // back to char
    }
    return c;   // non-letters unchanged
}

Why the four steps?

• Subtract 'a' to map letter to 0-25.
• Add amount to shift.
• Modulo 26 to wrap past 'z' back to 'a'.
• Add 'a' to convert back to a letter.

Shifting a whole String

public String encode(String s, int amount) {
    String result = "";
    for (int i = 0; i < s.length(); i++) {
        result += shift(s.charAt(i), amount);
    }
    return result;
}