# Bitwise operations
### Bitwise Operator quizzes
* [C Bitwise Operators Quiz](http://doc.callmematthi.eu/C_Bitwise_Operators.html)
* [線上測驗](https://pconrad.github.io/old_pconrad_cs16/topics/bitOps/) (附上解答)
### Set a bit
:::info
where n is the bit number, and 0 is the least significant bit
:::
```cpp
unsigned char a |= (1 << n);
```
Example:
```
a 1 0 0 0 0 0 0 0
a |= (1 << 1) = 1 0 0 0 0 0 1 0
a |= (1 << 3) = 1 0 0 0 1 0 0 0
a |= (1 << 5) = 1 0 1 0 0 0 0 0
```
### Clear a bit:
```cpp
unsigned char b &= ~(1 << n);
```
- [ ] Example 1:
```
b 1 1 1 1 1 1 1 1
b &= ~(1 << 1) = 1 1 1 1 1 1 0 1
b &= ~(1 << 3) = 1 1 1 1 0 1 1 1
b &= ~(1 << 5) = 1 1 0 1 1 1 1 1
```
- [ ] Example 2:
Write a macro with two arguments a and pos, where a is a byte and the pos specifies a bit position of the byte. The macro should clear the particular bit position in the given byte.
```cpp
#include <stdio.h>
/* bit clear:
a: int,
pos: bit position to clear */
#define CLEARBIT(a, pos) (a &= ~(1 << pos))
int main() {
/* 'z': decimal value 122 (=01111010) */
char a = 'z';
/* clearing the 5th bit */
char aOut = CLEARBIT(a, 5);
/* aOut = 'Z': decimal value 90 (=01011010) */
printf("aOut=%c\n", aOut);
return 0;
}
```
### Toggle a bit:
```cpp
unsigned char c ^= (1 << n);
```
Example:
```
c 1 0 0 1 1 0 1 1
c ^= (1 << 1) = 1 0 0 1 1 0 0 1
c ^= (1 << 3) = 1 0 0 1 0 0 1 1
c ^= (1 << 5) = 1 0 1 1 1 0 1 1
```
### Test a bit:
```cpp
unsigned char e = d & (1 << n); //d has the byte value.
```
### The right/left most byte
assuming 16 bit, 2-byte short integer:
```cpp
unsigned char right = val & 0xff; /* right most (least significant) byte */
unsigned char left = (val >> 8) & 0xff; /* left most (most significant) byte */
```
### sign bit
assuming 16 bit, 2-byte short integer, two's complement:
```cpp
bool sign = val & 0x8000; // sign bit
```
### Setting and Clearing a Bit
The code below shows how to set or clear a bit of an integer.
```cpp
#include <stdio.h>
#include <stdbool.h>
void binary(unsigned int n) {
for (int i = 256; i > 0; i /= 2) {
if (n & i)
printf(" 1");
else
printf(" 0");
}
printf("\n");
}
bool getBit(int n, int index) {
return ((n & (1 << index)) > 0);
}
int setBit(int n, int index, bool b) {
if (b)
return (n | (1 << index));
int mask = ~(1 << index);
return n & mask;
}
int main() {
int num = 16, index;
printf("Input\n");
for (int i = 7; i >= 0; i--)
printf("%d ", getBit(num,i));
printf("\n");
/* set bit */
index = 6;
printf("# Setting %d-th bit\n", index);
num = setBit(num, index, true);
for (int i = 7; i >= 0; i--)
printf("%d ", getBit(num,i));
printf("\n");
/* unset (clear) bit */
index = 4;
printf("# Unsetting (Clearing) %d-th bit\n", index);
num = setBit(num, index, false);
for (int i = 7; i >= 0; i--)
printf("%d ", getBit(num,i));
printf("\n");
return 0;
}
```
Output is:
```
Input
0 0 0 1 0 0 0 0
# Setting 6-th bit
0 1 0 1 0 0 0 0
# Unsetting (Clearing) 4-th bit
0 1 0 0 0 0 0 0
```
延伸閱讀: [Bitwise Operators in C](http://www2.mta.ac.il/~hbinsky/c%20content/Bits.pdf)
* Uses of Bitwise Operations or Why to Study Bits
* Compression
* Set operations
* Encryption
* The Magic of XOR
> `x ^ y == (~x & y) | (x & ~y)`
---
## Applications
* [2018Q1 考古題](https://hackmd.io/s/rJh9U4Guf) / [考古題參考解答](https://hackmd.io/s/S1f0tSyTG)
* [2018Q3 考古題](https://hackmd.io/s/S1a9-YO_Q) / [考古題參考解答](https://hackmd.io/s/By5KCaZam)
* [2019Q1 考古題](https://hackmd.io/@sysprog/SyrZMGYr4) / [考古題參考解答](https://hackmd.io/@chenishi/S1DHQ3KrE) / [延伸閱讀](https://medium.com/fcamels-notes/%E4%BD%BF%E7%94%A8%E4%BD%8D%E5%85%83%E8%A8%88%E7%AE%97%E5%8A%A0%E9%80%9F%E6%B1%82%E8%A7%A3-n-queen-d20442f34110)
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