agreed there is not enough info. please clarify. lacking that here is one interpretation; your ref may be using "+" to refer to binary OR ($\vee$), this is common in many refs. then we have the table
a + b = c
0 0 0
0 1 1
1 0 1
1 1 1
leading to a truth table (x is true iff the eqn A + B = C holds)
a b c x
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1
this can be encoded as four binary constraints but not fewer (proof exercise for reader):
$(A \vee B \vee \bar{C}) \wedge (A \vee \bar{B} \vee C) \wedge (\bar{A} \vee B \vee C) \wedge (\bar{A} + \bar{B} + C)$
however introducing auxiliary (free) variable D one can write using 3 boolean constraints:
$(C \vee \bar{D}) \wedge (\bar{A} \vee D) \wedge (\bar{B} \vee D)$
background: this is basically the same construction used in the Tseitin transform (exercise for reader to show the correspondence).