Logic Levels(H/L), Truth Values(T/F), Data Values(1/0)

Don't confuse these.  They are three different things.

Logic levels are measured in volts.  If there are two valid voltage ranges they are labelled H(igh) and L(ow).

Truth values are not physical quantities and cannot be measured.  They tell you if something is true or false (asserted or not). Logic values are T(rue) or F(alse).

Logic signals can be either active-high (T=H) or active-low (T=L).  Both conventions are commonly used, even within one IC or circuit.  Active-low signals are usually indicated with an overbar over the signal name or an asterisk after the signal name (RUN*).

Numbers are also non-physical quantities.  Single-digit binary values they can have values of 0 or 1.

There is no standard mapping from logic levels to truth values or numbers.  The value 1 can be represented by either H or L.

Computer languages deal with truth values (T/F) and data values (integers).  They do not deal with voltage levels (H/L). 

Not all computer languages have implicit conversion between truth values and integers.  But for those that do, the value F is almost always represented as 0 and T as 1 (or sometimes any non-zero value).