Converting 8 bits to a scaled 12 bits equivalent

Question

I need to convert an 8 bit number (0 - 255 or #0 - #FF) to its 12 bit equivalent (0 - 4095 or #0 - #FFF)

I am not wanting to do just a straight conversion of the same number. I am wanting to represent the same scale, but in 12 bits.

For example:-

0xFF in 8 bits should convert to 0xFFF in 12 bits

0x0 in 8 bits should convert to 0x0 in 12 bits

0x7F in 8 bits should convert to 0x7FF in 12 bits

0x24 in 8 bit should convert to 0x249 in 12 bits

Are there any specific algorithms or techniques that I should be using?

I am coding in C

Answer 1

Try x << 4 | x >> 4.

This has been updated by the OP, changed from x << 4 + x >> 4