Replacing a bit range

Question

Something any sophomore in CS should be able to answer, but I can't seem to wrap my head around it...

I have a set of bits, and I need to replace some of the bits with a different set. In a simplified example:

10101010 -original bit set

00001111 -mask showing replacement positions

00001100 -new bit values

10101100 -resulting bit set

Another example:

10101010 -original bit set

00110011 -mask

11111111 -new bit values

10111011 -resulting bit set

It's trivial to do this by iterating across the bits.

Is it possible to do this using boolean logic (AND, OR, etc.)?

Answer 1

result = (original & ~mask) | (newbits & mask)

The "& ~mask" part make sure to clear those bits to 0 before the | part.

The "& mask" part make sure that only proper bits in newbits are used.

Answer 2

Mask out the bits to be replaced out of the original (by ANDing with the NOT of the mask), then put the new bits in (via OR).

10101010 -original bit set

00001111 -mask showing replacement positions

00001100 -new bit values

11110000 -negated mask

10100000 -original bitset masked

10101100 -new bits put back in

---

In C(++) code, it would be:

out = (in & ~mask) | newbits;

If the newbits contain bits outside of what they're supposed to replace, AND them with the mask as well.

Answer 3

(NEW and MASK) OR (OLD and NOT MASK)