Where is the 6th bit in 16-bit char value?

Question

There are two examples of bit switching in the book Java: A Beginners Guide . In both cases, the author writes about switching the 6th bit but he demonstrates it on 16 digits. Both examples use bitwise operators for changing the letter case.

1. In the first, he operates on lower case characters: 'a' & 65503 changes the char to 'A' . It is described as switching the 6th bit off. The problem is the number 65503 equals 1111 1111 1101 1111 in binary. Hence the 11th digit/bit is switched off (he even shows the number there).
2. The same he does for uppercase letters and bitwise OR operator: 'a' | 32 'a' | 32 does the trick. The number 32 equals 0000 0000 0010 0000 in binary.

In both cases, the change does make sense. I just don't understand why the author writes about the 6th bit. I would understand if it was for the 11th bit or 6th pair (in that case I would expect the turning it off completely as 00 or 11 .

Any clarification more than welcome.

Answer 1

The location of the 6th bit could be in a few locations, depending upon the convention you adopt:

1. Counting the left-most bit as zero-th, and moving right
2. Counting the left-most bit as first, and moving right
3. Counting the right-most bit as zero-th, and moving left
4. Counting the right-most bit as first, and moving left
5. (Other conventions may be available)

The author should really have defined which of these he was using, for clarity (and may do, elsewhere in the text). But apparently, he means item 4.

0000 0000 0010 0000
            65 4321

Answer 2

The 0's and 1's that make up a binary number are called bits. The bits start from the right and go left:

So 0010 0000 :

8th bit  7th bit  6th bit  5th bit  4th bit  3rd bit  2nd bit  1st bit
0        0        1        0        0        0        0        0

Decimal is read the same way as binary:

3754 in decimal:

(3 x 1000) | (7 x 100) | (5 x 10) | (4 x 1)

156 in binary = 10011100

(1 x 128)|(0 x 64)|(0 x 32)|(1 x 16)|(1 x 8)|(0 x 4)|(0 x 2)|(0 x 1)

In decimal you add a new column to to the start of the number (ie the right) when you reach a power of 10.

In binary you add a new column when you reach a power of 2.

Does this help explain it?