MySql CASE expression with two input columns

Question

I'm looking to use a case expression in mysql with two columns as input. This is how I would like to format the code. All code snippets use Set @a = 0; Set @b = 0; at the start, although those values can be modified. My own use case has several values each could be (more than 2 each).

SELECT 
    CASE (@a , @b)
        WHEN (0 , 0) THEN 'Both zero'
        WHEN (1 , 0) THEN 'a is 1'
        WHEN (0 , 1) THEN 'b is 1'
        WHEN (1 , 1) THEN 'both 1'
        ELSE NULL
    END;

When using the case statement this way, MySql throws Error Code: 1241. Operand should contain 1 column(s). For reference, both of the following work, which makes me curious why the above doesn't.

SELECT 
    IF((@a , @b) = (0 , 0),
        'Both zero',
        IF((@a , @b) = (1 , 0),
            'a is 1',
            IF((@a , @b) = (0 , 1),
                'b is 1',
                IF((@a , @b) = (1 , 1), 'both 1', NULL))));

and

SELECT 
    CASE
        WHEN (@a , @b) = (0 , 0) THEN 'Both zero'
        WHEN (@a , @b) = (1 , 0) THEN 'a is 1'
        WHEN (@a , @b) = (0 , 1) THEN 'b is 1'
        WHEN (@a , @b) = (1 , 1) THEN 'both 1'
        ELSE NULL
    END;

So, the question: Can I use a CASE expression like the first code snippet when doing a multi-column comparison? If so, please provide an example. If not, why not?

The 3rd method is completely viable for my own use case, but if @a and @b were select statements, it wouldn't be. The ideal would be a solution that:

1. Only runs inputs once, if they were select statements.
2. Can be easily expanded upon for any number of inputs.
3. Is agnostic to the input types (IE (@a,@b) = (0,'!@#$:abc') is a valid case to check).

Answer 1

You can't use the short version of CASE with multiple values. You need to use the long version that tests both conditions with AND

CASE 
    WHEN @a = 0 AND @b = 0 THEN 'Both zero'
    WHEN @a = 1 AND @b = 0 THEN 'a is 1'
    WHEN @a = 0 AND @b = 1 THEN 'b is 1'
    WHEN @a = 1 AND @b = 1 THEN 'Both 1'
    ELSE NULL
END

Another option is to concatenate them.

CASE CONCAT(@a, @b)
    WHEN '00' THEN 'Both zero'
    WHEN '10' THEN 'a is 1'
    WHEN '01' THEN 'b is 1'
    WHWN '11' THEN 'Both 1'
    ELSE NULL
END