- Practice
- Algorithms
- Bit Manipulation
- 2's complement

# 2's complement

# 2's complement

Understanding *'s complement* representation is fundamental to learning about Computer Science. It allows us to write negative numbers in binary. The leftmost digit is used as a sign bit. If it is , we have a negative number and it is represented as the two's complement of its absolute value. Let's say you wrote down the 's complement representation for each -bit integer in the inclusive range from to . How many 's would you write down in all?

For example, using an -bit byte rather than bit integer, the two's complement of a number can be found by reversing all its bits and adding . The two's complement representations for a few numbers are shown below:

```
|Number| Representation in
Number Binary Inverse Two's Complement
-3 00000011 11111100 11111101
-2 00000010 11111101 11111110
-1 00000001 11111110 11111111
0 00000000 00000000
1 00000001 00000001
2 00000010 00000010
3 00000011 00000011
```

To write down that range of numbers' two's complements in bits, we wrote 's. Remember to use bits rather than in your solution. The logic is the same, so the bit representation was chosen to reduce apparent complexity in the example.

**Function Description**

Complete the *twosCompliment* function in the editor below. It should return an integer.

twosCompliment has the following parameter(s):

- *a*: an integer, the range minimum

- *b*: an integer, the range maximum

**Input Format**

The first line contains an integer , the number of test cases.

Each of the next lines contains two space-separated integers, and .

**Constraints**

**Output Format**

For each test case, print the number of 's in the -bit 's complement representation for integers in the inclusive range from to on a new line.

**Sample Input 0**

```
3
-2 0
-3 4
-1 4
```

**Sample Output 0**

```
63
99
37
```

**Explanation 0**

Test case 0

-2 has 31 ones

-1 has 32 ones

0 has 0 ones

31+32+0 = 63

Test case 1

-3 has 31 ones

-2 has 31 ones

-1 has 32 ones

0 has 0 ones

1 has 1 ones

2 has 1 ones

3 has 2 ones

4 has 1 ones

31+31+32+0+1+1+2+1 = 99

Test case 2

-1 has 32 ones

0 has 0 ones

1 has 1 ones

2 has 1 ones

3 has 2 ones

4 has 1 ones

32+0+1+1+2+1 = 37

**Sample Input 1**

```
4
-5 0
1 7
-6 -3
3 6
```

**Sample Output 1**

```
155
12
122
7
```

**Explanation 1**

Test case 0

-5 has 31 ones

-4 has 30 ones

-3 has 31 ones

-2 has 31 ones

-1 has 32 ones

0 has 0 ones

31+30+31+31+32+0 = 155

Test case 1

1 has 1 ones

2 has 1 ones

3 has 2 ones

4 has 1 ones

5 has 2 ones

6 has 2 ones

7 has 3 ones

1+1+2+1+2+2+3 = 12

Test case 2

-6 has 30 ones

-5 has 31 ones

-4 has 30 ones

-3 has 31 ones

30+31+30+31 = 122

Test case 3

3 has 2 ones

4 has 1 ones

5 has 2 ones

6 has 2 ones

2+1+2+2 = 7