BCD subtractor is a circuit which accepts minuend and subtrahend in the form of BCD and produces the difference in BCD form. The BCD subtractor will be implemented in this project with the help of a BCD adder and 9’s complement circuits. A schematic diagram of the design of the BCD Subtractor is shown in figure (1).
Must Read BCD Adder Circuit
Project
Circuit Diagram
Components Required
- 7483 4 Bit Adder (x4)
- 7404 NOT Gate (x2)
- 7432 OR Gate
- 7485 Magnitude Comparator
- 7486 EX-OR Gate
- Single Pole 2-Way Switch (x8)
- LED (x5)
- 5V Power Supply
- Breadboard
- Wires
About Parts of BCD Subtractor Circuit
IC-7486 EX-OR Gate
This is a Quad 2-input EX-OR gate with 14 pins IC. It is widely used in the arithmetic section of a computer. This gate is widely used in digital electronics design and therefore, is available in IC form. EX-OR has two inputs and an output. Output is 1 (High) only when the inputs are unequal and output is 0 (Low) when the inputs are the same. If this acts as an inequality detector. The pin diagram of the IC-7486 is shown in figure (2).
The Truth Table for IC-7486 X-OR Gate
| A | B | Y=A⊕B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
IC-7483 4-Bit Full Adder
The IC-7483 is a commonly available TTL 4-bit parallel adder chip. It contains four interconnected full adders; a look-ahead carry circuitry for its operation (CLA = Carry Look-Ahead Adder). The logic symbol of IC-7483 is shown in figure (3) and the pin configuration in table 1. It has two 4-bit A3, A2, A1, A0 and B3, B2, B1, B0 and a carry input Cin in the LSB stage. The outputs are a 4-bit sum S3, S2, S1, S0 and a carry output (Cout) from the MSB stage.
Two or more parallel adder blocks can be connected in a cascade to perform the addition operation on a larger binary number. The four LSB of the number is added in the first adder. The carry output of this adder is given as carrying input to the second adder, which adds the four MSB of the number. the output carry of the second adder is the final carry output.
IC-7404 NOT Gate
The IC-7404 is a logic gate IC. It consists of six NOT gates. We know that the NOT gate is also called an inverter because it does complement the input. When we apply zero or low signal to the input, it gives 1 or high signal as in the output. The pin diagram of the IC-7404 is shown in figure (4).
The Truth Table for IC-7404 NOT Gate
| Inputs | Outputs |
|---|---|
| X | x̄ |
| 0 | 1 |
| 1 | 0 |
IC-7485 4 bit Comparator
The IC-7485 is a 4-bit magnitude comparator of the TTL family. This IC compares the magnitudes of two 4-bit numbers; A3, A2, A1, A0. and B3, B2, B1, B0. This IC has three outputs (A>B)out, (A=B)out, and (A<B)out. Besides those pins, this IC has cascading facilities. These cascading inputs are (A>B)in, (A=B)in, and (A<B)in. When the two inputs are equal then the outputs of the chip become a function of cascading inputs.
IC-7432 OR Gate
The IC-7432 is a member of gate ICs and has the functionality of an OR gate or function. It will give high if either all or any one of the two inputs is high. IC-7432 has 4 OR gates of 2 inputs in 1 package. The internal gates are made of from Schottky Transistor of low power.
Circuit Connection for BCD Subtractor Circuit
- Firstly, for the 1st 9’s complement circuit we use the NOT Gate (IC-7404) and CLA (carry look-ahead) Adder IC (IC-7483).
- Secondly, for the middle BCD Adder part, we use two (IC-7483) CLA Adder, (IC-7485) 4-bit Magnitude comparator and one (IC-7432) OR Gate.
- Thirdly, for the last part i.e. 2nd 9’s complement circuit, we use the X-OR Gate (IC-7486) and CLA Adder IC (IC-7483).
PCB Design
For removing messy wiring and give a clean look, I designed a PCB prototype for this project. It is also helpful for troubleshooting that runs great without any errors. To design this PCB board, I used EasyEDA as it is too easy to use. For ordering PCB for this, I prefer PCBWay.
Gerber file for BCD subtractor Circuit Gerber.
PCB View
Order PCB From PCBWay
There are so many forums or communities for electronics online in today’s technical world, and one of the famous ones for PCB manufacturing is PCBWay. PCBWay is a place that brings manufacturers and customers together. They have more than a decade of experience in this field of fabrication, prototyping and assembling PCBs. PCBWay has proved its focus on its customers’ needs in terms of cost-effectiveness, delivery, and quality.
How PCB Manufacturing Process Done in PCBWay
Standard quality for any product needs to be maintained using some parameters. PCBWay gives that opportunity through quality control in designing and manufacturing. At first, they ensure the accuracy, clarity, and validity of the PCB files that we sent to them.
Then all the boards will go through the most stringent tests other than the basic visual check. They adopt most of the testing and inspecting equipment used in the industry, such as Flying Probe Tester, X-Ray Inspection Machine, and Automated Optical Inspection (AOI) Machine. PCBWay are having 50+ new engineers on the daily basis around the world using PCBs for their work, who trust for their reliable quality. They produce high-quality pink, orange, grey, and even transparent solder mask. Moreover, according to people’s needs, they can also provide Black core PCB. Check it out for a High-Quality PCB solder mask. There are some pictures below of the new colours of solder musks.
Features of PCBWay
PCB Prototyping & Manufacturing: PCBWay produces FR-4 and Aluminum boards and advanced PCBs like Rogers, HDI, Flexible and Rigid-Flex boards, at a very reasonable price. Just check this Instant Quote to order premium PCBs for your hobby projects.
PCB Assembly: It not only offers PCB Prototyping but also offers PCB Assembly service. You can order a full PCB board with attached components by uploading your file. SMT & THT assembly starts from only 30$ including free stencil and worldwide shipping. The components can be sourced and provided by PCBWay, or by clients themselves.
Open Source Community: It not only offers PCB Prototype & Assembly service but also gives opportunities to students for sponsorships. I think this is so great. They feature their projects on the website also.
3D Printing & CNC: It also produces Rapid Prototyping like 3D printing, CNC Machining, Sheet Metal Fabrication, and Injection Molding. The quality of the product is too premium and reliable. And also the best part is that you will receive your order within a minimum of 3 days.
PCBWay Store: More boutique gift modules are waiting for you to discover, giving your creativity wings. You can order all types of electronic equipment, components and many more with exciting offers. Go with the link and buy your needs, PCBWay Store.
Services: PCBWay offers great servicing of their products. It takes only 3 to 15 days according to courier service to deliver your products. Also, it has a live support facility. Whenever you have any problems, you can always reach a live customer service person to respond to your emails or messages. They have the “Return and Refund” principle, for every unusable board caused by PCBWay, they will rebuild and refund the order soon.
Guide for Ordering PCB From PCBWay
Working Principle of BCD Subtractor Circuit
The working principle of this project is quite complicated, so read this carefully. In subtractor, one 9’s complement circuit is used to produce the 9’s complement of the BCD subtrahend Y (Y3 Y2 Y1 Y0). The output of the 9’s complement circuit is used as one of the two inputs of the BCD adder. The other input of this BCD adder is connected directly to the BCD minuend. The second 9’s complement circuit is connected to the sum of the output of the BCD adder which generates the 9’s complement of the BCD adder output if the EN(=Cout) input of the second 9’s complement circuit is 1 otherwise for EN=0 i.e., Cout = 1, the 9’s complement circuit passes the sum output of the BCD adder unchanged. This type of 9’s complement circuit is shown below.
The action of this single decade BCD subtractor can be understood from the following discussion.
There may be two cases that may arrive:
- BCD minuend (X) ≤ BCD subtrahend (Y)
- BCD minuend (X) > BCD subtratend
In both cases,
A input of the BCD adder = Minuend = X
B input of the BCD adder = 9’s complement of the subtrahend = 9-Y
Case (1): X≤Y
Sum output of the BCD adder. Then X + (9- Y) + Cin + BCD correction factor (if needed).
As X≤Y, the sum X+ (9-Y) can never exceed 9 because the maximum value of X and y is 9.
Therefore, carry output from the BCD adder = Cout=0 and hence, carry input Cin is 0 and as Cin and Cout are connected.
The BCD correction in the adder unit is not needed when Cout = 0 because the sum from the full adder unit of this BCD adder is X+(9-Y)≤9.
The enable input (EN) of the second 9’s complement circuit = Cout=1, so the output of the second 9’s complement generator circuit is 9-{X+(9-Y)} = (Y-X).
Hence, the output of the 9’s complement circuit gives the magnitude and the output of the NOT Gate is 1. This output indicates the negative sign.
Case (2): X>Y
In this case, the sum X+(9-Y) always exceeds 9, so the BCD correction factor within the BCD adder will be 6.
Carry output from the BCD adder is Cout=1 and hence the Cin=1.
Sum output of the BCD adder= X+(9-Y) +1+6 = (X-Y)+16.
The factor 16 indicates that Cout=1. If this Cout is ignored then the sum output from the BCD adder will be (X-Y) and as Cout=1, the enable input of the second 9’s complement circuit is 0. Therefore, the output of this 9’s complement circuit will be (X-Y).
The Theoretical Truth Table for the subtraction of two BCD numbers and getting the result in BCD
| X3 | X2 | X1 | X0 | Y3 | Y2 | Y1 | Y0 | EN (sign) | S3 | S2 | S1 | S0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
Precautions & Discussions for BCD Subtractor Circuit
- Various resistance should be chosen in the conduction state current through the LED. So that it doesn’t exceed the maximum rated current. So carefully choose the safety resistance.
- The experiment has been done by using +ve level logic where a high voltage i.e. equal to (+VCC) i.e., +5V is taken as ‘1’ and a low voltage i.e., equal to GND i.e., 0V is taken as ‘0’.
- LEDs with proper current limiting resistance can be used for easy, quick and visual identification of ‘0’ and ‘1’ states. If the LED glow then it is in an on state and if it doesn’t glow then it is in an off state.
- While connecting the 5V DC supply to the IC special care should be taken. Connection to any wrong pin any damage maybe happen.
- Carefully connect the pins bitwise from comparators IC-7485 and IC-7483. For any wrong correction, the output will not be as we want to get.
- For the BCD Subtractor circuit, we are using two 9’s complement circuits, one at the first point i.e., before the BCD adder and the other is just after the BCD adder circuit.
- Special care should be taken during setting up the wire connection to LSB and MSB bit so that the output should be in the correct form otherwise it goes wrong.