on numToHex(n, res)
    -- Round the input value to the nearest whole-number. (Just in case it's fractional.)
    set n to n div 0.5 - n div 1

    script o
        property hexDigits : missing value
        property hexOut : {}
    end script

    if (n > -1) then
        -- The number's positive.
        set o's hexDigits to {"0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "A", "B", "C", "D", "E", "F"}

        -- Construct a list of the hexadecimal digits, working backwards from the lowest-order one.
        set widthNow to 0
        repeat
            set beginning of o's hexOut to item (n mod 16 + 1) of o's hexDigits
            set n to n div 16
            set widthNow to widthNow + 1
            -- Finish when n is exhausted and the digit count is a multiple of the resolution. 
            if (n is 0) and (widthNow mod res is 0) then exit repeat
        end repeat
    else
        -- The number's negative.
        set o's hexDigits to {"1", "2", "3", "4", "5", "6", "7", "8", "9", "A", "B", "C", "D", "E", "F", "0"}
        set negatives to "89ABCDEF"

        -- Construct a list of the hexadecimal digits, working backwards from the lowest-order one.
        set widthNow to 0
        repeat
            set c to item (n mod 16 - 1) of o's hexDigits
            set beginning of o's hexOut to c
            set n to (n + 1) div 16 - 1
            set widthNow to widthNow + 1
            -- Finish when n is exhausted, the digit count is a multiple of the resolution,
            -- and the first digit in the list expresses the negative sign bit. 
            if (n is -1) and (widthNow mod res is 0) and (c is in negatives) then exit repeat
        end repeat
    end if

    -- Coerce the digit list to string.
    set astid to AppleScript's text item delimiters
    set AppleScript's text item delimiters to ""
    set hexOut to o's hexOut as string
    set AppleScript's text item delimiters to astid

    return hexOut
end numToHex