Obviously, w = 3/2 x + 1/4 y + z = x + (x >> 1) + (y >> 2) + z. But, this is not the end of the story.
All variables here need to be interpreted as fixed point number, with lower 2 digits representing 0.5 and 0.25.
Let’s say x, y and z are within the range between 0 and 3, inclusive. Then w is within the range between 0 and 8.25, inclusive. w’s integer part has 4 bits, and w has 6 bits in total.
‘d8.25 can be represented as ‘b1000.01