# Counting One in Binary Expression

## Question

Given a number, find the number of 1 in the number’s binary expression. For example, binary express of 10 is 1010. So the number of 1 in it is 2.

## Solution

To solve this, we can check each bit by shifting the bits one by one.

- 1010 -> check 0
- 101 -> check 1
- 10 -> check 0
- 1 -> check 1

So how to check it? we could use the AND function.

- 1010 -> check 1010 & 1 = 0
- 101 -> check 101 & 1 = 1 -> counter + 1
- 10 -> check 10 & 1 = 0
- 1 -> check 1 & 1 = 1 -> counter + 1

However, negative number will put this program into infinite loop. For example, shifting -10 (0xFFFFFFF6) several times gives 0xFFFFFFFF. Then shifting 0xFFFFFFFF will give 0xFFFFFFFF and makes infinite loops. Therefore instead of shifting the inputting number, we should shift the comparing number.

- 1010 -> check 1010 & 1 = 0
- 1010-> check 1010 & 10 = 1 -> counter + 1
- 1010 -> check 1010 & 100 = 0
- 1010 -> check 1010 & 1000 = 1 -> counter + 1

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