Half subtractor and Full subtractor

1. Half Subtractor:

A combinational logic circuit known as a half subtractor conducts subtraction for two 1-bit binary integers. The minuend (A) and the subtrahend (B) are its two inputs, while the difference (D) and the borrow (Borrow) are its two outputs. The truth table for the half subtractor is as follows:

| A | B | Difference (D) | Borrow |

|---|---|---------------|--------|

| 0 | 0 |       0       |   0    |

| 0 | 1 |       1       |   1    |

| 1 | 0 |       1       |   0    |

| 1 | 1 |       0       |   0    |

The borrow output (Borrow) indicates whether a borrow is necessary during the subtraction operation, while the difference output (D) displays the result of A - B. When subtracting larger binary integers, the borrow output is utilized as an input to the following step.

2. Full Subtractor:

Three 1-bit binary integers, A (minuend), B (subtrahend), and the preceding borrow (Bin), are subtracted using a complete subtractor, a more complex combinational logic circuit. The differential (D) and the new borrow (Bout) are its two outputs from a system with three inputs. The truth table for the entire subtractor is as follows:

| A | B | Bin | Difference (D) | Borrow Out (Bout) |

|---|---|-----|---------------|-------------------|

| 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          |

The result of (A - B) - Bin is given by the difference output (D), and the borrow output (Bout) shows whether a borrow is necessary for the subtraction operation. When subtracting even larger binary integers, the borrow out is fed into the following stage as an input.

Building blocks for developing larger subtractors in digital circuits include the half subtractor and full subtractor. They are essential for performing mathematical operations and are utilized in CPUs and other digital systems to do subtraction operations.