Digital Electronics/Mathematic and Logic Operations/Digital Subtractor
< Digital Electronics < Mathematic and Logic OperationsHalf Subtractor
The half-subtractor is a combinational circuit which is used to perform subtraction of two bits. It has two inputs, X (minuend) and Y (subtrahend) and two outputs D (difference) and B (borrow).
Truth Table
The truth table for the half subtractor is given below. [1]
| X | Y | D | B |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
From the above table one can draw the Karnaugh map for "difference" and "borrow".
Full Subtractor
The full subtractor is a combinational circuit which is used to perform subtraction of three bits. It has two inputs, X (minuend) and Y (subtrahend and Z (subtrahend) and two outputs D (difference) and B (borrow).
Truth Table
The truth table for the full subtractor is given below. [2]
| X | Y | Z | D | B |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
So, logic equations are D = (X xor Y)xor Z, B = (Z and (not(X xor Y)))or ((not X)and Y)
References
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