Update

bit.md

@@ -0,0 +1,233 @@
+# Bit
+
+## & operator
+
+AND bit by bit
+
+[#bit](bit.md)
+
+## << operator
+
+Shift on the left
+
+n * 2 <=> left shift by 1
+n * 4 <=> left shift by 2
+
+[#bit](bit.md)
+
+## >> operator
+
+Shift on the right
+
+[#bit](bit.md)
+
+## >>> operator
+
+Logical shift (shift the sign bit as well)
+
+[#bit](bit.md)
+
+## ^ operator
+
+XOR bit by bit
+
+[#bit](bit.md)
+
+## Bit vector structure
+
+Vector (linear sequence of numeric values stored contiguously in memory) in which each element is a bit (so either 0 or 1)
+
+[#bit](bit.md)
+
+## Check exactly one bit is set
+
+```java
+boolean checkExactlyOneBitSet(int num) {
+	return (num & (num - 1)) == 0;
+}
+```
+
+[#bit](bit.md)
+
+## Clear bits from i to 0
+
+```java
+int clearBitsFromITo0(int num, int i) {
+	int mask = (-1 << (i + 1));
+	return num & mask;
+}
+```
+
+[#bit](bit.md)
+
+## Clear bits from most significant one to i
+
+```java
+int clearBitsFromMsbToI(int num, int i) {
+	int mask = (1 << i) - 1;
+	return num & mask;
+}
+```
+
+[#bit](bit.md)
+
+## Clear ith bit
+
+```java
+int clearBit(final int num, final int i) {
+	final int mask = ~(1 << i);
+	return num & mask;
+}
+```
+
+[#bit](bit.md)
+
+## Flip ith bit
+
+```java
+int flipBit(final int num, final int i) {
+	return num ^ (1 << i);
+}
+```
+
+[#bit](bit.md)
+
+## Get ith bit
+
+```java
+boolean getBit(final int num, final int i) {
+	return ((num & (1 << i)) != 0);
+}
+```
+
+[#bit](bit.md)
+
+## How to flip one bit
+
+b ^ 1
+
+[#bit](bit.md)
+
+## How to represent signed integers
+
+Use the most significative bit to represent the sign. Yet, it is not enough (problem with this technique: 5 + (-5) != 0)
+
+Two's complement technique: take the **one complement and add one**
+
+-3: 1101
+-2: 1110
+-1: 1111
+0:  0000
+1:  0001
+2:  0010
+3:  0011
+
+The **most significant** bit still represents the **sign**
+
+Max integer value: 1...1 (31 bits)
+-1: 1...1 (32 bits)
+
+[#bit](bit.md)
+
+## Set ith bit
+
+```java
+int setBit(final int num, final int i) {
+	return num | (1 << i);
+}
+```
+
+[#bit](bit.md)
+
+## Update a bit from a given value
+
+- Clear this bit
+- Apply OR on the result with a 0 or 1 left shifted to its index
+
+```java
+int updateBit(int num, int i, boolean bit) {
+	int value = bit ? 1 : 0;
+	int mask = ~(1 << i);
+	return (num & mask) | (value << i);
+}
+```
+
+[#bit](bit.md)
+
+## x & 0s
+
+0
+
+[#bit](bit.md)
+
+## x & 1s
+
+x
+
+[#bit](bit.md)
+
+## x & x
+
+x
+
+[#bit](bit.md)
+
+## x ^ 0s
+
+x
+
+[#bit](bit.md)
+
+## x ^ 1s
+
+~x
+
+[#bit](bit.md)
+
+## x ^ x
+
+0
+
+[#bit](bit.md)
+
+## x | 0s
+
+x
+
+[#bit](bit.md)
+
+## x | 1s
+
+1s
+
+[#bit](bit.md)
+
+## x | x
+
+x
+
+[#bit](bit.md)
+
+## XOR operations
+
+0 ^ 0 = 0
+1 ^ 0 = 1
+0 ^ 1 = 1
+1 ^ 1 = 0
+
+n XOR 0 => keep
+n XOR 1 => flip
+
+[#bit](bit.md)
+
+## | operator
+
+OR bit by bit
+
+[#bit](bit.md)
+
+## ~ operator
+
+Complement bit by bit
+
+[#bit](bit.md)