can I convert an integer to base-2 without a function
Unless I'm completely misunderstanding your question, then the below T-SQL should do it (please let me know if this isn't what you're looking for).  It utilizes bitwise operators to pull out the bit masks for the days:

-- &lt;TEST DATA&gt;
create table DayTable
(
    id int identity(1, 1) not null,
    DayMask tinyint not null
)
go

insert into DayTable
values
(
    62
),
(
    12
)
-- &lt;/TEST DATA&gt;

select
        case 
            when DayMask &amp; 1 &gt; 0
                then 1
            else 0
        end
    as Sunday,
        case 
            when DayMask &amp; 2 &gt; 0
                then 1
            else 0
        end
    as Monday,
        case 
            when DayMask &amp; 4 &gt; 0
                then 1
            else 0
        end
    as Tuesday,
        case 
            when DayMask &amp; 8 &gt; 0
                then 1
            else 0
        end
    as Wednesday,
        case 
            when DayMask &amp; 16 &gt; 0
                then 1
            else 0
        end
    as Thursday,
        case 
            when DayMask &amp; 32 &gt; 0
                then 1
            else 0
        end
    as Friday,
        case 
            when DayMask &amp; 64 &gt; 0
                then 1
            else 0
        end
    as Saturday
from DayTable