notArefill - 1 year ago 124

C Question

I'm trying to learn C on my own. I came across this exercise and i am studying to understand it. I have read about masking bits and in order to get the last four bits we should do val&0xF.I have read this post as well What is Masking?. The part that i need an explanation is why the possible values are 0x7,0xB,0xD,0xE,0xF. I am studying the answer and i have read various articles. If someone is willing to explain to me this part i would appreciate it.

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Answer Source

Because these are all the possible numbers with at least three of the last four bits on. If you write down every binary number from 0 to 15, you will see that these have at least three of the last four bits set:

- 0111 (0x7)
- 1011 (0xB)
- 1101 (0xD)
- 1110 (0xE)
- 1111 (0xF)

Think of it like this: every binary number from 0 to 6 has at most 2 bits set:

- 0 (0)
- 1 (1)
- 10 (2)
- 11 (3)
- 100 (4)
- 101 (5)
- 110 (6)

Thus, none of it matches the rule. From 7 up to 15, we have:

- 111 (7)
- 1000 (8)
- 1001 (9)
- 1010 (10)
- 1011 (11)
- 1100 (12)
- 1101 (13)
- 1110 (14)
- 1111 (15)

From these, only 7, 11, 13, 14 and 15 have three of the last four bits set.

This method is easy to implement:

```
int chk_last_bits2(unsigned x) {
return ((x & 0x7) == 0x7) ||
((x & 0xB) == 0xB) ||
((x & 0xD) == 0xD) ||
((x & 0xE) == 0xE) ||
((x & 0xF) == 0xF);
}
```

Note that we have to explicitly test for equality for each case. For example, `x & 0xB`

will return a non-zero value for every number with any of `1011`

bits set. This is not what we want, we want all of them to be on, which can be tested with equality.

Another possible solution would be:

```
int chk_last_bits(unsigned x) {
int i, j;
for (i = 1, j = 0; i < 32; i <<= 1)
if (i & x)
j++;
return j >= 3;
}
```

Since you're learning C, I'll leave this one for you to try to understand.