The circuit shown in figure has 4 boxes each described by inputs P, Q, R and outputs Y, Z with
Y = $$\,P \oplus \,Q\, \oplus \,R$$
z= $$RQ + \overline P R\, + Q\,\overline P $$ The circuit acts as a

The circuit shown in figure converts

In the TTL circuit in Figure 2.11, $${S_0}$$ to $${S_0}$$ are select lines and $${X_7}$$ and $${X_0}$$are input lines. $${S_0}$$ and $${X_0}$$ are LSB'. The output Y is

For a binary half-sub-tractor having two inputs A and B, the correct set of logical expressions for the outputs D (=A minus B) and X (=borrow) are