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Reversible logic gates Aneesh Raveendran
aneeshr2020@gmail.com
- 1 - Centre for Development of Advanced Computing(C-DAC)
INDIA
REVERSIBLE COMPUTING
1. Introduction:
Many researchers believe that Moore’s law is at an end. The power requirements of
traditional methods used to increase performance are too great. Laundauer’s principle
states that logic computations that are not reversible generate kT ln 2 Joules of heat
energy for every bit of information energy that is lost. It has been proven that using
traditional irreversible logic gates necessarily leads to power dissipation regardless of
underlying technology. A reversible logic design will not result in information loss; this
avoids the unwanted heat generated. For power not to be dissipated in an arbitrary
circuit, it must be built from reversible gates.
2. Reversible Gates:
A digital combinational logic circuit is reversible if it maps each input pattern to a unique
output pattern. There are many types of reversible gates including: inverter/NOT,
Feynman, Toffoli, and Fredkin. Table 1 lists the behavior of each of these reversible
gates.
Table 1: Gate functionality
Reversible logic gates Aneesh Raveendran
aneeshr2020@gmail.com
- 2 - Centre for Development of Advanced Computing(C-DAC)
INDIA
2.1 Not Gate:
The most primitive of logic gates, the one-input one-output not gate simply inverts the
logic value of the input on its output.
------------------------------------------------------------------------------------------------------------
library ieee;
use ieee.std_logic_1164.all;
entity rev_not is port (
a : in std_logic;
x : out std_logic);
end rev_not;
architecture config of rev_not is
begin
process(a)
begin
if (a=’0’) then
x<=’1’;
else
x<=’0’;
end if;
end process;
end config;
------------------------------------------------------------------------------------------------------------
2.2 Feynman Gate:
When A = 0 then Q = B, when A = 1 then Q = B’. The Feynman Gate can be used as a fan-
out/copying gate or an XOR gate where BAQ ⊕= .
Figure 1: Feynman gate
Reversible logic gates Aneesh Raveendran
aneeshr2020@gmail.com
- 3 - Centre for Development of Advanced Computing(C-DAC)
INDIA
------------------------------------------------------------------------------------------------------------
library ieee;
use ieee.std_logic_1164.all;
entity feynman is port (
a : in std_logic;
b : in std_logic;
p : out std_logic;
q : out std_logic);
end feynman;
architecture config of feynman is
begin
process(a, b)
begin
p <= a;
q <= a xor b;
end process;
end config;
------------------------------------------------------------------------------------------------------------
2.3 Toffoli Gate:
Both A and B inputs are passed directly though the gate to P and Q outputs respectively.
The R output uses more complex logic, ABCR ⊕= . By setting C = 0, it becomes an
AND gate R = AB.
Figure 2: Toffoli gate
------------------------------------------------------------------------------------------------------------
library ieee;
use ieee.std_logic_1164.all;
entity toffoli is port (
a : in std_logic;
b : in std_logic;
Reversible logic gates Aneesh Raveendran
aneeshr2020@gmail.com
- 4 - Centre for Development of Advanced Computing(C-DAC)
INDIA
c : in std_logic;
p : out std_logic;
q : out std_logic;
r : out std_logic);
end toffoli;
architecture config of toffoli is
begin
process(a, b, c)
begin
p <= a;
q <= b;
r <= c xor (a and b);
end process;
end config;
------------------------------------------------------------------------------------------------------------
Reversible logic gates Aneesh Raveendran
aneeshr2020@gmail.com
- 5 - Centre for Development of Advanced Computing(C-DAC)
INDIA
2.4 Fredkin Gate:
In this gate, the input signals A and B are routed to the same or exchange putout ports
depending on the value of the control signal C.
Figure 3: Fredkin gate
------------------------------------------------------------------------------------------------------------
library ieee;
use ieee.std_logic_1164.all;
entity fredkin is port (
a : in std_logic;
b : in std_logic;
c : in std_logic;
p : out std_logic;
q : out std_logic;
r : out std_logic);
end fredkin;
architecture config of fredkin is
begin
process(a, b, c)
begin
p <= c;
q <= (a and not(c)) or (b and c);
r <= (b and not(c)) or (a and c);
end process;
end config;
------------------------------------------------------------------------------------------------------------

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Reversible Logic Gate

  • 1. Reversible logic gates Aneesh Raveendran aneeshr2020@gmail.com - 1 - Centre for Development of Advanced Computing(C-DAC) INDIA REVERSIBLE COMPUTING 1. Introduction: Many researchers believe that Moore’s law is at an end. The power requirements of traditional methods used to increase performance are too great. Laundauer’s principle states that logic computations that are not reversible generate kT ln 2 Joules of heat energy for every bit of information energy that is lost. It has been proven that using traditional irreversible logic gates necessarily leads to power dissipation regardless of underlying technology. A reversible logic design will not result in information loss; this avoids the unwanted heat generated. For power not to be dissipated in an arbitrary circuit, it must be built from reversible gates. 2. Reversible Gates: A digital combinational logic circuit is reversible if it maps each input pattern to a unique output pattern. There are many types of reversible gates including: inverter/NOT, Feynman, Toffoli, and Fredkin. Table 1 lists the behavior of each of these reversible gates. Table 1: Gate functionality
  • 2. Reversible logic gates Aneesh Raveendran aneeshr2020@gmail.com - 2 - Centre for Development of Advanced Computing(C-DAC) INDIA 2.1 Not Gate: The most primitive of logic gates, the one-input one-output not gate simply inverts the logic value of the input on its output. ------------------------------------------------------------------------------------------------------------ library ieee; use ieee.std_logic_1164.all; entity rev_not is port ( a : in std_logic; x : out std_logic); end rev_not; architecture config of rev_not is begin process(a) begin if (a=’0’) then x<=’1’; else x<=’0’; end if; end process; end config; ------------------------------------------------------------------------------------------------------------ 2.2 Feynman Gate: When A = 0 then Q = B, when A = 1 then Q = B’. The Feynman Gate can be used as a fan- out/copying gate or an XOR gate where BAQ ⊕= . Figure 1: Feynman gate
  • 3. Reversible logic gates Aneesh Raveendran aneeshr2020@gmail.com - 3 - Centre for Development of Advanced Computing(C-DAC) INDIA ------------------------------------------------------------------------------------------------------------ library ieee; use ieee.std_logic_1164.all; entity feynman is port ( a : in std_logic; b : in std_logic; p : out std_logic; q : out std_logic); end feynman; architecture config of feynman is begin process(a, b) begin p <= a; q <= a xor b; end process; end config; ------------------------------------------------------------------------------------------------------------ 2.3 Toffoli Gate: Both A and B inputs are passed directly though the gate to P and Q outputs respectively. The R output uses more complex logic, ABCR ⊕= . By setting C = 0, it becomes an AND gate R = AB. Figure 2: Toffoli gate ------------------------------------------------------------------------------------------------------------ library ieee; use ieee.std_logic_1164.all; entity toffoli is port ( a : in std_logic; b : in std_logic;
  • 4. Reversible logic gates Aneesh Raveendran aneeshr2020@gmail.com - 4 - Centre for Development of Advanced Computing(C-DAC) INDIA c : in std_logic; p : out std_logic; q : out std_logic; r : out std_logic); end toffoli; architecture config of toffoli is begin process(a, b, c) begin p <= a; q <= b; r <= c xor (a and b); end process; end config; ------------------------------------------------------------------------------------------------------------
  • 5. Reversible logic gates Aneesh Raveendran aneeshr2020@gmail.com - 5 - Centre for Development of Advanced Computing(C-DAC) INDIA 2.4 Fredkin Gate: In this gate, the input signals A and B are routed to the same or exchange putout ports depending on the value of the control signal C. Figure 3: Fredkin gate ------------------------------------------------------------------------------------------------------------ library ieee; use ieee.std_logic_1164.all; entity fredkin is port ( a : in std_logic; b : in std_logic; c : in std_logic; p : out std_logic; q : out std_logic; r : out std_logic); end fredkin; architecture config of fredkin is begin process(a, b, c) begin p <= c; q <= (a and not(c)) or (b and c); r <= (b and not(c)) or (a and c); end process; end config; ------------------------------------------------------------------------------------------------------------