# Half Subtractor and Full Subtractor VHDL Simulation Code

Experiment: Write a VHDL code for half subtractor and full subtractor and simulate the code.

Introduction:
To develop code for half subtractor and full subtractor. Simulate the code in the software.

Material required:
1. Xilinx Software Loaded PC = 1 Set.
2. Print = 1.

Description:
1. Theory
2. Algorithm
3. Description
4. VHDL Code Writing
5. Compile and Run program.

Theory:
The Half-Adder is a basic building block of adding two numbers as two inputs and produce out two outputs. The adder is used to perform OR operation of two single bit binary numbers.

ALGORITHM:
1. Define Library functions.
2. Declare Entity and Architecture.
3. Describe functionality.
4. End source code.
5. Compile and Run program.

DESCRIPTION:
The augent and addent bits are two input states, and ‘carry’ and ‘sum ‘are two output states of the half adder.

Half-subtractor circuit

TRUTH TABLE

VHDL Code for a Half-Subtractor

```library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.STD_LOGIC_ARITH.ALL;
use IEEE.STD_LOGIC_UNSIGNED.ALL;
Library ieee;
use ieee.std_logic_1164.all;

entity half_sub is
port ( a,b : in std_logic;
dif,bo: out std_logic );
end half_sub;
architecture sub_arch of half_sub is
begin
dif <= a xor b;
bo <= (not a) and b;
end sub_arch;
```

Full-Subtractor
The Half Subtractor is used to subtract only two numbers. To overcome this problem, a full subtractor was designed. The full subtractor is used to subtract three 1-bit numbers A, B, and C, which are minuend, subtrahend, and borrow, respectively. The full subtractor has three input states and two output states i.e., diff and borrow.

Full-Subtractor circuit:

```library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.STD_LOGIC_ARITH.ALL;
use IEEE.STD_LOGIC_UNSIGNED.ALL;

entity full_sub is
port(a,b,c: in bit; sub, borrow:out bit);
end full_sub;

architecture data of full_sub is
begin
sub<= a xor b xor c;
borrow <= ((b xor c) and (not a)) or (b and c);
end data;
```

TRUTH TABLE

VHDL Code for a Full-Subtractor
VHDL program to build half and full-subtractor circuits. Verify the output waveform of program (digital circuit) with the truth tables for the half and full-subtractor circuits.

Half-subtractor Output

Full-subtractor Output

1. What is the half-subtractor?
Ans: The half-subtractor is a combinational circuit which is used to perform subtraction of two bits.

2. What is the Full-subtractor?
Ans: A full subtractor is a combinational circuit that performs subtraction involving three bits, namely A (minuend), B (subtrahend), and Bin (borrow-in) . It accepts three inputs.

3. What is half-subtractor boolean expression?
Ans: Difference = A ⊕ B
Borrow = A’ B

4. What is Full-subtractor boolean expression
Ans: D = A ⊕ B ⊕ Bin
Bout = A’ Bin + A’ B + B Bin

Half Subtractor Video Tutorial:

Full Subtractor Video Tutorial:

##### Subramanian

Subramanian MK, currently serving as a workshop instructor at Sakthi Polytechnic College, Erode Tamil Nadu. With a career spanning 25 + years, Subramanian MK has dedicated himself to advancing knowledge in Electronics and Communication Engineering (ECE). His passion for exploring new technologies has led to the development of numerous projects, showcasing expertise in IoT and PCB design.

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