The BCD adder to add two decimal digits needs minimum of

Explanation

To add two BCD digits we need two 4-bit adders: the first adds the two BCD numbers and the second corrects the result to a valid BCD number. The first 4-bit adder needs 3 full adders and 1 half adder (giving A₃ A₂ A₁ A₀). In the correction step 0110 is added to A₃ A₂ A₁ A₀. A₀ is always added to 0, so no adder is needed; A₁ is added to 1 with no incoming carry, so a half adder is used; A₂ is added to 1 plus a carry, so a full adder is used; A₃ is added only to the carry, so a half adder is used. Total = 3 + 1 = 4 full adders and 1 + 2 = 3 half adders.