Binary Adders Section 3 8 Mano Kime Binary
Binary Adders Section 3 -8 Mano & Kime
Binary Adders • Review half adder and full adder from CSE 171 • VHDL Adder
Half Adder A 0 B 0 S 0 0 0 1 1 0 1 0 1 1 0 A 0 B 0 C 1 0 0 0 1 S 0 C 1 Dec Binary 1 +1 2 1 +1 10
Multiple-bit Addition A 3 A 2 A 1 A 0 B 3 B 2 B 1 B 0 A 0 1 A B B 0 1 1 0 0 1 1 1 0 0 Ci+1 +Ci Ai +Bi Si
Full Adder Ci Ai Bi Si Ci+1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 Ai B i 00 C i 11 1 01 10 1 1 1 Si
Full Adder Ci Ai Bi Si Ci+1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 Si = # # # !Ci & !Ai & Bi !Ci & Ai & !Bi Ci & !Ai & !Bi Ci & A i & B i
Full Adder Si = # # # !Ci & !Ai & Bi !Ci & Ai & !Bi Ci & !Ai & !Bi Ci & A i & B i Si = !Ci & (!Ai & Bi # Ai & !Bi) # Ci & (!Ai & !Bi # Ai & Bi) Si = !Ci & (Ai $ Bi) # Ci & !(Ai $ Bi) Si = Ci $ (Ai $ Bi)
Full Adder Ci Ai Bi Si Ci+1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 Ai B i 00 C i 01 10 1 11 1 1 Ci+1 1
Full Adder Ci Ai Bi Si Ci+1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 Ai B i 00 Ci 01 10 1 11 1 Ci+1 = Ai & Bi # Ci & B i # Ci & A i
Full Adder Ci Ai Bi Si Ci+1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 Ai B i 00 Ci 01 10 1 11 1 Ci+1 = Ai & Bi # Ci & !Ai & Bi # Ci & Ai & !Bi
Full Adder Ci+1 = Ai & Bi # Ci !Ai & Bi # Ci & Ai & !Bi Ci+1 = Ai & Bi # Ci & (!Ai & Bi # Ai & !Bi) Ci+1 = Ai & Bi # Ci & (Ai $ Bi) Recall: Si = Ci $ (Ai $ Bi) Ci+1 = Ai & Bi # Ci & (Ai $ Bi)
Full Adder Si = Ci $ (Ai $ Bi) Ci+1 = Ai & Bi # Ci & (Ai $ Bi) Half-adder
Full Adder A full adder can be made from two half adders (plus an OR gate).
Full Adder Block Diagram
4 -Bit Adder C A B S 1 0 0 1 1 1 0 1 0 0 1 1 0
Binary Adders • Review half adder and full adder from CSE 171 • VHDL Adder
Adder in VHDL entity adder is port ( a: in STD_LOGIC_VECTOR (3 downto 0); b: in STD_LOGIC_VECTOR (3 downto 0); sum: out STD_LOGIC_VECTOR (3 downto 0); carry: out STD_LOGIC ); end adder;
std_logic_arith. vhd
Ai B i 00 Ci 01 10 1 11 1 Ci+1 = Ai & Bi # Ci & B i # Ci & A i
std_logic_unsigned. vhd
adder. vhd
Binary Multiplier Half Adders are Sufficient Since there is no Carry-in in addition to the two inputs to sum 2 bit by 2 bit
Binary Multiplier 4 bit by 3 bit yields 7 bit result
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