Subtractor Circuit – Half Subtractor, Full Subtractor & Applications

Arithmetic Subtraction of binary digits is performed using Subtractor Circuit. This post will discuss about what is Subtractor Circuit, it’s types (Half Subtractor and Full Subtractor), its Applications, Advantages and Disadvantages.

What is Subtractor Circuit

Subtractor Circuit is a combinational logic circuit that performs subtraction on binary numbers. As the digits involved in Binary Notation are 0 and 1, subtraction of ‘0’ from a ‘0’ or ‘1’ does not change the result. ‘1’ subtracted from ‘1’ results in ‘0’. Subtracting ‘1’ from ‘0’ requires borrow.

Fig. 1 – Introduction to Subtractor Circuit

Fig. 2 shows 2-bit Subtractor which has 2 inputs A, B. This circuit produces Difference and Borrow bit. The circuit consists of an Adder with inverters placed between each data input and B_in (Borrow) input of the previous stage of Full Adder.

Fig. 2 – Block Diagram of Full-Subtractor Circuit

Types of Subtractor Circuit

There are two types of subtractor circuit. They are:

• Half Subtractor
• Full Subtractor

Half Subtractor

Two single bit binary numbers can be subtracted by using Half Subtractor circuit. This circuit needs two binary inputs ‘A’ and ‘B’ to produce two binary outputs ‘D’ and ‘b’. ‘A’ bit is Minuend, ‘b’ bit is Subtrahend. The output bit ‘D’ is the difference bit and ‘b’ is Borrow bit.

Let us create Truth Table for different values of input A and B.

Fig. 3 – Truth Table Representation of Half-Subtractor 

For the above Truth Table entries, K-Maps is drawn to determine the Boolean expression.

Fig. 4 – K-Map Representation of Half-Subtractor 

D is an EX-OR gate and Borrow (b) is ‘And’ gate with complemented input A. When the output of half-adder and half- subtractor is compared, the Boolean expressions for SUM and Difference outputs are the same.

Fig. 5 – Logic Diagram of Half Subtractor 

Full Subtractor

Full Subtractor logic circuit performs subtraction on three-bit binary numbers. It is implemented by using two Half Subtractor circuits along with OR gate. This circuit has three inputs A, B and B_in. B_in is the borrow-in bit from the previous stage. It produces two output bits D and B_out.

D is the Difference bit and B_out is the borrow out bit. B_out indicates that the minuend bit requires borrow 1 from the consequent or subsequent minuend bit. Let us create Truth Table for different values of inputs A, B, B_in.

Fig. 6 – Truth Table Representation of Full Subtractor 

For the above Truth Table entries, K-Maps is drawn to determine the Boolean expression.

Fig. 7 – K-Map Representation of Full-Subtractor 

When this circuit is compared with Full Adder, we observe that Difference output is same as the Sum Output. The implementation of the circuit is done using 1 XOR gate, 3 AND gates, 1 NOT gate and 1 OR gate as shown below:

Fig. 8 – Logic Diagram of Full Subtractor 

How does Subtractor Circuit Work

The circuit is assembled as per the circuit diagram. DIP switches and resistors are connected to the inputs and LED’s are connected to the outputs. Hexadecimal Display is also connected to Output.

Power of 5V is applied at V_cc. Mode and Operation is selected according to the application. Here Mode=Operation= 1. The logic state of the outputs indicated by LED’s are noted for each input combination. Logic High = 1 = LED glows and Logic Low = 0 = LED is off. The results obtained are verified with the entries of the Truth-Table.

Fig. 9 shows simple ALU (subtractor) that performs subtraction result of A – B and the subtraction of two 4-bit numbers will not exceed 8 bits. The result is displayed in Binary by LED’s and in Hex by Seven Segment Display.

Fig. 9 – Subtraction Operation on ALU

Applications of Subtractor Circuit

The applications include:

• It is used in ALU (Arithmetic Logic Unit) and CPU (Central Processing Unit)
• They are widely used in electronic calculators and in devices like timers and program counters.
• They are also used in Digital Signal Processing.

Advantages of Subtractor Circuit

The advantages are:

• It is simple to design and implement.
• Power deduction in Digital Signal Processing.
• Computational tasks can be carried out at high speed.

Disadvantages of Subtractor Circuit

The disadvantages are:

• In case of half subtractor, there is no provision for accepting Borrow as input from the previous stage.
• The speed of the subtractor is limited by the longest delay through the circuit.

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