Question
Download Solution PDFWhich Boolean expression correctly represents the Difference (D) output of a Full Subtractor?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
The correct option for the Boolean expression that correctly represents the Difference (D) output of a Full Subtractor is Option 2: D = A ⊕ B ⊕ Bin.
A Full Subtractor is a combinational logic circuit used to perform the subtraction of three bits: the minuend (A), subtrahend (B), and the borrow-in (Bin). The Full Subtractor has two outputs: the Difference (D) and the Borrow-out (Bout).
Full Subtractor Truth Table:
| A | B | Bin | D (Difference) | Bout (Borrow-out) |
|---|---|---|---|---|
| 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 Difference (D) output can be derived from the truth table. The Boolean expression for the Difference (D) in a Full Subtractor is given by:
D = A ⊕ B ⊕ Bin
The XOR (⊕) operation is used because it outputs true (1) when an odd number of inputs are true (1). This property makes it ideal for calculating the difference in a subtraction operation.
Analysis of Other Options:
- Option 1: D = A ⊕ B ⊕ Cout - This option is incorrect because Cout (Carry-out) is not part of the inputs for calculating the Difference (D) in a Full Subtractor. The correct inputs are A, B, and Bin (Borrow-in).
- Option 3: D = A ⊕ B - This option is incorrect because it does not account for the Borrow-in (Bin) input, which is essential in the subtraction process in a Full Subtractor.
- Option 4: D = A AND B - This option is incorrect because the AND operation does not correctly represent the difference calculation. The correct operation involves the XOR function to handle the subtraction logic.
- Option 5: (Blank Option) - This option is not applicable as it does not provide any expression.
In summary, the correct Boolean expression for the Difference (D) output of a Full Subtractor is D = A ⊕ B ⊕ Bin, as it correctly considers all necessary inputs and their respective operations to perform the subtraction.
Last updated on Jun 7, 2025
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