3-Bit Binary Number Analyzer
Three independent gate networks report even values, B2 OR (B1 XOR B0), and values at least 3. These functions follow the executable wiring, including places where canvas annotations are inconsistent.
What You'll Learn
- Read B2B1B0 as a 3-bit value from 0 through 7.
- Derive Even directly from the least-significant bit.
- Derive the exact Pattern and AtLeast3 equations from their gates.
- Verify all eight stable input vectors and identify mislabeled requirements.
- Compare path depth and possible transition behavior across parallel outputs.
How It Works
The production circuit accepts a 3-bit number B2B1B0 and drives three output lights through three independent branches. It contains three switches, one NOT, one AND, one XOR, two OR gates, and three lights—11 non-text components. There is no digit display.
- Even = ¬B0. The top light is high for 0, 2, 4, and 6. - Pattern = B2 + (B1 ⊕ B0). The middle light is high for 1, 2, 4, 5, 6, and 7. - AtLeast3 = B2 + B1·B0. The lower light is high for 3 through 7.
The canvas annotation calls the middle result “powers of 2,” but the connected OR from B2 makes 5, 6, and 7 high as well. It also describes the threshold as B2 = 1 (at least 4), while the connected B1·B0 term deliberately adds 3. The equations and truth table here follow the executable component graph rather than those contradictory annotations.
This makes the template especially useful for engineering verification: derive each output from its wires, enumerate all eight input states, and test the requirement labels against the implemented functions instead of assuming they agree.
Truth Table
All eight values of B2B1B0 are shown. Outputs follow the actual equations Even = ¬B0, Pattern = B2 + (B1⊕B0), and AtLeast3 = B2 + B1·B0.
| Inputs | Output | |||||
|---|---|---|---|---|---|---|
| B2 | B1 | B0 | Even | Pattern | AtLeast3 | |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 (000): even; neither Pattern nor AtLeast3 asserted. |
| 0 | 0 | 1 | 0 | 1 | 0 | 1 (001): odd; Pattern asserted by the lower-bit XOR. |
| 0 | 1 | 0 | 1 | 1 | 0 | 2 (010): even; Pattern asserted by the lower-bit XOR. |
| 0 | 1 | 1 | 0 | 0 | 1 | 3 (011): odd; lower bits match, so Pattern is low, while AtLeast3 is high. |
| 1 | 0 | 0 | 1 | 1 | 1 | 4 (100): even; B2 asserts both Pattern and AtLeast3. |
| 1 | 0 | 1 | 0 | 1 | 1 | 5 (101): odd; B2 keeps Pattern and AtLeast3 high. |
| 1 | 1 | 0 | 1 | 1 | 1 | 6 (110): even; B2 keeps Pattern and AtLeast3 high. |
| 1 | 1 | 1 | 0 | 1 | 1 | 7 (111): odd; B2 keeps Pattern and AtLeast3 high. |
Boolean Expression
A binary integer is even exactly when its least-significant bit B0 is 0.
The middle light is high when B2 is high or B1 and B0 differ. This is the production circuit's exact pattern function.
B2 covers values 4–7, while B1·B0 adds value 3, so the lower light detects values greater than or equal to 3.
Try It Step-by-Step
Set the listed controls in the embedded circuit, then compare the observed modeled state with the expected result.
- 1B=000Expected:
Even = 1, Pattern = 0, AtLeast3 = 0What you'll see:000 drives Even high and leaves both multi-gate branches low. - 2B=011Expected:
Even = 0, Pattern = 0, AtLeast3 = 1What you'll see:011 proves the lower branch includes value 3, while the middle XOR term is 0. - 3B=100Expected:
Even = 1, Pattern = 1, AtLeast3 = 1What you'll see:100 is a genuine power of two and drives both Pattern and AtLeast3 high through B2. - 4B=111Expected:
Even = 0, Pattern = 1, AtLeast3 = 1What you'll see:111 also drives Pattern high, demonstrating that the middle branch is not a power-of-two detector.
Components Used
Applications and Design Context
Parity-independent even tests. The least-significant bit directly determines divisibility by two for binary integers.
Threshold decoding. Small comparators can be minimized into compact AND/OR expressions such as B2 + B1·B0.
Pattern recognition. XOR and OR networks classify selected input sets for control or diagnostics.
Specification verification. Exhaustive truth tables expose differences between labels, intended behavior, and implemented wiring.
Control-status generation. Several properties of one input word can be computed concurrently on independent combinational branches.
Frequently Asked Questions
Does the middle light detect powers of two?
No. Its equation is Pattern = B2 + (B1 ⊕ B0), so it is high for 1, 2, 4, 5, 6, and 7. A true 3-bit power-of-two detector must be high only for 001, 010, and 100, which requires an exactly-one-bit-set function.
Why does even detection use only B0?
In binary, B0 has weight 1. Values with B0 = 0 are divisible by two, so one inverter is sufficient: Even = ¬B0.
How does the circuit detect values at least 3?
Every value with B2 = 1 is 4–7. When B2 = 0, only 011 should meet the threshold; B1·B0 detects that case. ORing the terms gives B2 + B1·B0, which is high for 3–7.
Is there a decimal digit display in this template?
No. The production graph has three switches and three output lights but no digit-display component. Add a compatible display and connect B0–B2 according to its pin contract if a numeric readout is required.
Do the analyzer outputs have identical timing?
The XOR/OR Pattern path has two gate levels, as does the AND/OR AtLeast3 path for B0 and B1; the direct B2 threshold path has one. A timed implementation can therefore have unequal delays and transition hazards even when every stable truth-table row is correct.