Bit Hacks – Part 4 (Playing with letters of the English alphabet)

This post will discuss some bit hacks/tricks on letters of the English alphabet.

The following tricks are covered in this post:

Convert uppercase character to lowercase.
Convert lowercase character to uppercase.
Invert alphabet’s case.
Find a letter’s position in alphabet.

Trick 1. Convert uppercase character to lowercase

We can easily convert an uppercase character to a corresponding lowercase character by taking its bitwise OR with a space.

// Convert uppercase character to lowercase

for (char ch = 'A'; ch <= 'Z'; ch++) {

cout << char(ch | ' ')); // prints abcdefghijklmnopqrstuvwxyz

}

Trick 2. Convert lowercase character to uppercase

Similarly, we can easily convert a lowercase character to a corresponding uppercase character by taking its bitwise AND with an underscore character.

// Convert lowercase character to uppercase

for (char ch = 'a'; ch <= 'z'; ch++) {

cout << char(ch & '_')); // prints ABCDEFGHIJKLMNOPQRSTUVWXYZ

}

Trick 3. Invert alphabet’s case

The above-discussed methods will not work the other way, i.e., (ch | ' ') cannot convert lowercase alphabet to uppercase. The result will always be lowercase even if the letter is already lowercase. Similarly, (ch & '_') cannot convert the uppercase alphabet to lowercase. The result will always be uppercase even if the letter is already uppercase.

How can we invert the alphabet’s case?

We can easily convert an alphabet’s case by taking its bitwise XOR with a space.

// Convert lowercase alphabet to uppercase

for (char ch = 'a'; ch <= 'z'; ch++) {

cout << char(ch ^ ' ')); // prints ABCDEFGHIJKLMNOPQRSTUVWXYZ

}

// Convert uppercase alphabet to lowercase

for (char ch = 'A'; ch <= 'Z'; ch++) {

cout << char(ch ^ ' ')); // prints abcdefghijklmnopqrstuvwxyz

}

How does above solutions work?

The trick lies in ASCII codes of A–Z and a–z:

‘A’ — 01000001 ‘a’ — 01100001
‘B’ — 01000010 ‘b’ — 01100010
‘C’ — 01000011 ‘c’ — 01100011
‘D’ — 01000100 ‘d’ — 01100100
‘E’ — 01000101 ‘e’ — 01100101
and so on…

If we carefully analyze, we will notice that the ASCII codes of lowercase and uppercase characters differ only in their third significant bit. For uppercase characters, the bit is 0, and for lowercase characters, the bit is 1. If we could find a way to set/unset that particular bit, we can easily invert any character’s case. Now space ' ' has an ASCII code of 00100000 and '_' has an ASCII code of 01011111.

If we take bitwise OR of an uppercase character with ' ', the third significant bit will be set, and we will get its lowercase equivalent.
If we take bitwise AND of a lowercase character with '_', the third significant bit will be unset, and we will get its uppercase equivalent.
If we take bitwise XOR of an uppercase or lowercase characters with ' ' (ASCII 00100000), only its third significant bit will be toggled, i.e., lowercase becomes uppercase and vice versa.

Trick 4. Find a letter’s position in alphabet

We can easily find a letter’s position [1-26] in the alphabet by taking its bitwise AND with ASCII 31 (00011111 in binary). The case of the letter is irrelevant here. The explanation is left for the users as an exercise.

For example,

(‘A’ & 31) returns position 1
(‘c’ & 31) returns position 3

Reference:

https://stackoverflow.com/questions/1533131/what-useful-bitwise-operator-code-tricks-should-a-developer-know-about

Also See:

Bit Hacks – Part 1 (Basic)
Bit Hacks – Part 2 (Playing with k’th bit)
Bit Hacks – Part 3 (Playing with the rightmost set bit of a number)
Bit Hacks – Part 5 (Find the absolute value of an integer without branching)