Sometimes, there is more than one way to do something in VHDL. OK, most of the time, you can do things in many ways in VHDL. Let's look at the situation where you want to assign different values to a signal, based on the value of another signal.

With / Select

The most specific way to do this is with as selected signal assignment. Based on several possible values of a, you assign a value to b. No redundancy in the code here. The official name for this VHDL with/select assignment is the selected signal assignment.

with a select b <=
    "1000" when "00",
    "0100" when "01",
    "0010" when "10",
    "0001" when "11";

When / Else Assignment

The construct of a conditional signal assignment is a little more general. For each option, you have to give a condition. This means that you could write any boolean expression as a condition, which give you more freedom than equality checking. While this construct would give you more freedom, there is a bit more redundancy too. We had to write the equality check (a =) on every line. If you use a signal with a long name, this will make your code bulkier. Also, the separator that's used in the selected signal assignment was a comma. In the conditional signal assignment, you need the else keyword. More code for the same functionality. Official name for this VHDL when/else assignment is the conditional signal assignment

b <= "1000" when a = "00" else 
     "0100" when a = "01" else 
     "0010" when a = "10" else 
     "0001" when a = "11";

Combinational Process with Case Statement

The most generally usable construct is a process. Inside this process, you can write a case statement, or a cascade of if statements. There is even more redundancy here. You the skeleton code for a process (begin, end) and the sensitivity list. That's not a big effort, but while I was drafting this, I had put b in the sensitivity list instead of a. Easy to make a small misstake. You also need to specify what happens in the other cases. Of course, you could do the same thing with a bunch of IF-statements, either consecutive or nested, but a case statement looks so much nicer.

process(a)
begin
    case a is
        when "00" => b <= "1000";
        when "01" => b <= "0100";
        when "10" => b <= "0010";
        when "11" => b <= "0001";
        when others => report "unreachable" severity failure;
    end case;
end process;

While this last code snippet is the largest and perhaps most error-prone, it is probably also the most common. It uses two familiar and often-used constructs: the process and the case statements.

Hard to remember

The problem with the selected and conditional signal assignments is that there is no logic in their syntax. The meaning is almost identical, but the syntax is just different enough to throw you off. I know many engineers who permanenty have a copy of the Doulos Golden Reference Guide to VHDL lying on their desks. Which is good for Doulos, because their name gets mentioned all the time. But most people just memorize one way of getting the job done and stick with it.