Usual arithmetic conversions in C : Whats the rationale behind this particular rule

Question

From k&R C

• First, if either operand is long double, the other is converted to long double.
• Otherwise, if either operand is double, the other is converted to double.
• Otherwise, if either operand is float, the other is converted to float.
• Otherwise, the integral promotions are performed on both operands; ...

This would mean below expression

char a,b,c;

c=a+b;

is actually caculated as

c = char((int)a+(int)b);

What is the rationale behind this rule?

Do these conversions happen if a, b and c were short ?