Digital Logic Fundamentals Binary Division Hardware Designing

Question

Assume that 'a' and 'y' are 8-bit signals with the std_logic_vector (7 downto 0) data type. If the signals are interpreted as unsigned numbers, the following assignment statement performs a / 8. Explain. y <= “000” & a(7 downto 3); This question is in RTL Hardware designing chapter 3 Problem 3.6. I have the answer of this problem and that is by shifting three times right to any binary value will be divisible by 8 but i don't know how .? Can anyone explain this .?

Answer 1

Look at the simpler case of calculating a/2. Shifting the bits right means they move to a position with half the value as the previous one.

Examples:

110 (binary) = 6 (decimal)  shifted to  011 (binary) = 3 (decimal)

101 (binary) = 5                        010          = 2 (decimal).

The last example showed 5/2=2.5 automagically truncated into 2 since the least significant bit was shifted out.

To get a/8, just repeat a/2 three times ie shift down three positions. In hardware, this is usually done by "moving the wires", in this case by wiring bits (7 downto 3) into position (4 downto 0) and filling the upper three bits with zeros.