# Bit mathematics cookbook

November 29, 2018

I found this amazing cookbook written by Joel Yliluoma a.k.a *bisqwit*.
Just check it if you are interested in bit operations, and it is highly recommended if you work in embedded engineering.
**Note** Two’s complement is assumed.

Here is an example of Addition without carry

```
// Using subtraction
uint_type a = original_1;
uint_type b = original_2;
b = -b;
uint_type result = a - b;
// Using bitwise operations, with XOR
uint_type a = original_1;
uint_type b = original_2;
uint_type carry = a & b;
uint_type result = a ^ b;
while(carry != 0) {
// If you need the mathematical carry from addition,
// check the overflow from this shift.
uint_type shiftedcarry = carry << 1;
carry = result & shiftedcarry;
result = result ^ shiftedcarry;
}
```

That guy is sick.