## JoãoVitorMC 2 years ago How many bits must be “flipped” (i.e., changed from 0 to 1 or from 1 to 0) in order to capitalize a lowercase ‘a’ that’s represented in ASCII?

1. eSpeX

Do you know the decimal value for each of the characters?

2. eSpeX

Take the decimal equivalent to your ascii, convert to binary, compare the results.

3. nick67

@JoãoVitorMC it's more useful to start from hex values: A <=> 41 <=> 0100 0001 a <=> 61 <=> 0110 0001 B <=> 42 <=> 0100 0010 b <=> 62 <=> 0110 0010 ... ... Z <=> 5A <=> 0101 1010 z <=> 7A <=> 0111 1010 just toggle b5 from 0 to 1 to transform uppercase to lowercase or toggle b5 from 1 to 0 to transform from lowercase to uppercase: that's all

4. myndless

going from lowercase to uppercase in ascii is equivalent to subtracting 32 from the decimal notation of the lowercase letter. 'a' = 97, 97-32 = 65 = 'A'. Subtracting 32 is equivalent to doing an XOR with 00100000, with the possibility of a carry bit in the case that you XOR a 0 with a 1, which could in turn trigger a bit flip, which means that at most the 3 most significant bits could flip. However, the lowercase alphabet in ASCII is only 97-122 in decimal. That entire range begins with 011 in binary, thus subtracting 00100000 will always only flip the '32' place bit. So not only for 'a', but for all 26 letters in the english alphabet, exactly 1 bit must be flipped to capitalize it in ASCII.