## Half Subtractor-

• Half Subtractor is a combinational logic circuit that is used for the purpose of subtracting two single bit numbers.
• It contains 2 inputs and 2 outputs (difference and borrow). ## Designing a Half Subtractor-

### Step-01:

Identify the input and output variables-

• Input variables = A , B (either 0 or 1)
• Output variables = D , b where D = Difference and b = borrow

### Step-02:

Draw the truth table-

 Inputs Outputs A B D (Difference) b (borrow) 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0

Truth Table

### Step-03:

Draw the K-maps using the above truth table and determine the simplified Boolean expressions- ### Step-04:

Draw the logic diagram- Logic Diagram

Here, Half Subtractor has been implemented using 1 XOR gate, 1 NOR gate and 1 AND gate.

## Limitation of Half Subtractor-

Half Subtractors do not take into account “Borrow-in” from the previous circuit when we perform the subtraction of multiple number of bits.

This is a major drawback of half subtractors because real time scenarios involve subtracting the multiple number of bits which can not be accomplished using half subtractors.

To overcome this drawback, Full Subtractor comes into play.

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