Parallel Adders

Parallel Adders

Objective:

  1. To understand how FA can be cascaded to for adding multi-bit numbers.
  2. To develop VHDL code for design of VHDL Code in different style of modeling
  3. To synthesize and simulate the parallel adders

Theory:

A Full adder is a combinational circuit that adds two one bit numbers along with a carry from the lower stage and produces  the sum and the carry as output.

This 1-bit FA can be cascaded to perform multi-bit addition. The block diagram shown below gives details of multibit addition.

Figure: Block diagram showing multi-bit addition process

 

To perform addition of two n-bit addition:

  1. set the carry in bit to ‘0’
  2. connect cout of first stage FA to Cin of next stage FA and so on.
  3. Connect Ai, Bi to Fi; wher i is the FA stage and bit position of two number

VHDL Code for Parallel Adders

structural Modeling

AIM: Design a 4-bit Full adder using 1-bit full adder in VHDL using structural modelling

library IEEE;

use IEEE.STD_LOGIC_1164.ALL;

entity fa1_4bit is

Port (

a : in  STD_LOGIC_VECTOR (3 downto 0);

b : in  STD_LOGIC_VECTOR (3 downto 0);

ci : in  STD_LOGIC;

s : out  STD_LOGIC_VECTOR (3 downto 0);

co : out  STD_LOGIC

);

end fa1_4bit;

architecture structural of fa1_4bit is

componentfullAdder is

Port (

a : in  STD_LOGIC;

b : in  STD_LOGIC;

ci : in  STD_LOGIC;

s : out  STD_LOGIC;

co1 : out  STD_LOGIC

);

end component;

signal carry : std_logic_vector(3 downto 1);

begin

X1: fullAdder PORT MAP (a(0), b(0), ci, s(0), carry(1));

X2: fullAdder PORT MAP (a(1), b(1), carry(1), s(1), carry(2));

X3: fullAdder PORT MAP ( a => a(2), b => b(2), ci=> carry(2), s=> s(2), co1=> carry(3));

X4: fullAdder PORT MAP ( a => a(3), b => b(3), ci=> carry(3), s=> s(3), co1=> co);

End structural;

 

Simulation of 4-bit Adder

Figure:- simulation of a 4-bit adder

 

4-bit adder using Generate

 

AIM: Design a 4-bit Full adder using 1-bit full adder in VHDL using GENERATE Statement

library IEEE;

use IEEE.STD_LOGIC_1164.ALL;

entity fa1_4bit is

Port (

a : in  STD_LOGIC_VECTOR (3 downto 0);

b : in  STD_LOGIC_VECTOR (3 downto 0);

ci : in  STD_LOGIC;

s : out  STD_LOGIC_VECTOR (3 downto 0);

co : out  STD_LOGIC

);

end fa1_4bit;

architecture Behavioral of fa1_4bit is

component FA1 is

Port (

a : in  STD_LOGIC;

b : in  STD_LOGIC;

ci : in  STD_LOGIC;

s : out  STD_LOGIC;

co1 : out  STD_LOGIC

);

end component;

signal carry : std_logic_vector(4 downto 0);

begin

carry (0) <= ci;

x1: for I in 0 to 3 GENERATE

X2: FA1 PORT MAP (

a(i), b(i), carry(i), s(i), carry(i+1)

);

end GENERATE;

co<= carry(4);

end Behavioral;

Simulation

Simulation of 4-bit Adder synthesized using Generate Statement

Figure:-4-bit adder generate ..simulation

 

RCA Behavioral Style

 

A-n-bit RCA is a simple chain of FAs. For N-bit adder, it consist N full adder  connected in series through their carry-in and carry-out ports, Each FA adds three bits Ai, Bi, and Cin to produce two bit ouput Si and Cout bits.

Because the carry must propagate (ripple) through all the stages serially, this is the slowest adder architecture.

Roughly, the time required by the FA units to compute the carry out bit is two gate delays per FA units, thus total delay  in generating the final carry Cout is 2xN (2x number of FA) .

Figure: Ripple Carry Addition Process

 

The values in Gray color (A3A2A1A0, B3B2B1B0  and C0 )are given while in circles (C4C3C2C1 and S3S2S1S0 )are computed. The simplest multi-bit adder is the Ripple carry adder, shown below.

 

Figure: – 4-bit Ripple Carry Adder

 

library IEEE;

use IEEE.STD_LOGIC_1164.ALL;

entity fa1_4bit is

Port (     a : in  STD_LOGIC_VECTOR (3 downto 0);

b : in  STD_LOGIC_VECTOR (3 downto 0);

ci : in  STD_LOGIC;

s : out  STD_LOGIC_VECTOR (3 downto 0);

co : out  STD_LOGIC);

end fa1_4bit;

 

architecture Behavioral of fa1_4bit is

signal carry : std_logic_vector(4 downto 0);

begin

carry (0) <= ci;

for I in 0 to 3 LOOP

s(i) <= a(i) xor b(i) xor carry(i);

carry (i+1) <= (a(i) and b(i)) or (b(i) and carry(i)) or (carry(i) and a(i));

end LOOP;

co<= carry (4);

end Behavioral;

 

 

Updated: August 11, 2019 — 9:56 am

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