Calculator Input
Enter two operands, choose arithmetic, comparison, and logic options, then submit.
Example Data Table
This table shows sample input sets and likely study cases.
| Operand A | Operand B | Base | Bits | Arithmetic | Comparison | Logic | Use Case |
|---|---|---|---|---|---|---|---|
| 25 | 9 | Decimal | 8 | A + B | A > B | AND | Basic ALU lab |
| 1101 | 0110 | Binary | 4 | A - B | A ≠ B | XOR | Truth table review |
| FF | 01 | Hex | 8 | A + B | A ≥ B | NAND | Carry flag test |
| 17 | 5 | Decimal | 16 | A mod B | A < B | OR | Remainder study |
Formula Used
Arithmetic Formula
The arithmetic section uses the selected operation on two operands.
Raw result = A operation B Masked result = Raw result AND ((2^n) - 1)
Comparison Formula
The comparison section returns a Boolean result.
Comparison result = A comparator B
Bitwise Logic Formula
The logic section compares each bit position separately.
AND = A & B OR = A | B XOR = A ^ B NAND = NOT(A & B) NOR = NOT(A | B) XNOR = NOT(A ^ B)
Flag Formula
Zero flag = masked result equals 0 Sign flag = most significant bit equals 1 Carry flag = unsigned result exceeds bit range Overflow flag = signed result exceeds signed range Parity flag = even count of 1 bits
How to Use This Calculator
- Enter operand A and operand B.
- Select the input base that matches your numbers.
- Choose a bit width for masking and flag checks.
- Select unsigned or signed two's complement mode.
- Choose arithmetic, comparison, logic, and shift options.
- Press the calculate button.
- Review the result above the form.
- Use CSV or PDF export for reports.
Understanding Arithmetic Logic Unit Calculations
What This Tool Models
An arithmetic logic unit is a core idea in computer architecture. It performs arithmetic work and logical decisions. This calculator models that behavior with practical inputs. You can add, subtract, multiply, divide, compare, shift, and test bitwise logic. It is useful for students, teachers, and developers. It also helps when checking low level number behavior.
Why Bit Width Matters
Real digital circuits use fixed bit sizes. An 8 bit result cannot store the same range as a 16 bit result. When a value becomes too large, the extra bits are removed. This is called masking. The masked result shows what remains inside the chosen register size. This is important for carry and overflow study.
Signed and Unsigned Values
Unsigned mode treats every bit as part of a positive number. Signed two's complement mode reserves the highest bit for the sign. This changes how the same binary pattern is interpreted. For example, an 8 bit value of 11111111 can mean 255 in unsigned mode. It can also mean -1 in signed mode.
Logic and Comparisons
Logical comparisons answer true or false questions. These include equal, not equal, greater than, and less than. Bitwise logic works differently. It compares each matching bit from both operands. AND keeps bits that are set in both values. OR keeps bits set in either value. XOR keeps bits that differ.
Flags and Reports
Status flags summarize the result. The zero flag shows a zero result. The sign flag checks the top bit. The carry flag is useful for unsigned arithmetic. The overflow flag is useful for signed arithmetic. The parity flag checks whether the count of one bits is even. Export options help save the calculation.
FAQs
1. What does this calculator do?
It models an arithmetic logic unit. It calculates arithmetic results, comparisons, bitwise logic, shifts, binary output, hexadecimal output, and common status flags.
2. What is an arithmetic logic unit?
It is a digital circuit block that performs arithmetic operations and logic operations. It is commonly discussed in computer architecture and processor design.
3. Why does the masked result differ from the raw result?
The masked result fits the selected bit width. Extra bits are removed, similar to fixed size registers in digital systems.
4. What is signed two's complement mode?
Signed two's complement mode interprets the highest bit as part of a negative value representation. It is common in modern binary arithmetic.
5. What does the carry flag mean?
The carry flag means an unsigned arithmetic operation exceeded the selected bit range. It is most useful for addition and subtraction.
6. What does the overflow flag mean?
The overflow flag means the signed result moved outside the selected signed range. It helps detect two's complement arithmetic issues.
7. Can I enter binary or hexadecimal values?
Yes. Choose the matching input base first. Binary, octal, decimal, and hexadecimal inputs are supported for both operands.
8. Can I export the result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple printable report.