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Assignment
[Checkbox symbol]Compute the truth table for the following combinational logics
**Chart/Diagram Description:**
The image contains two digital logic circuit diagrams.
**Circuit Diagram 1:**
* **Type:** Digital Logic Circuit Diagram.
* **Inputs:** Two inputs, labeled A and B, represented by circles.
* **Gates/Blocks:**
* Two rectangular boxes labeled '1'. One box has input A and an output line connected to point C. The other box has input B and an output line connected to point D.
* Two AND gates, labeled '&'.
* One OR gate, labeled '>=1'.
* Two inverters, represented by circles on the input lines of the AND gates.
* **Intermediate Points/Labels:** C and D are labeled on lines originating from the outputs of the '1' boxes.
* **Connectivity:**
* Input A is connected to the first box labeled '1', whose output line is labeled C. The same line C connects to an inverter, which is an input to the bottom AND gate. The input A is also directly connected to the top AND gate.
* Input B is connected to the second box labeled '1', whose output line is labeled D. The same line D connects to an inverter, which is an input to the top AND gate. The input B is also directly connected to the bottom AND gate.
* The top AND gate has inputs from A and the inverted signal from D.
* The bottom AND gate has inputs from B and the inverted signal from C.
* The outputs of the top and bottom AND gates are connected as inputs to the OR gate.
* **Output:** One output, labeled F, from the OR gate, represented by a circle.
**Circuit Diagram 2:**
* **Type:** Digital Logic Circuit Diagram.
* **Inputs:** Two inputs, labeled A and B, represented by circles.
* **Gates:**
* Three AND gates, labeled '&'.
* One inverter, represented by a circle on an input line of an AND gate.
* **Intermediate Points/Labels:** C is labeled on a line originating from the input line A.
* **Connectivity:**
* Input A is connected to the top AND gate. The input line A also connects to point C.
* Input B is connected to the bottom AND gate.
* Point C is connected as an input to the bottom AND gate.
* Point C is also connected to the inverter, whose output is an input to the top AND gate.
* The outputs of the top and bottom AND gates are connected as inputs to the third (final) AND gate.
* **Output:** One output, labeled F, from the final AND gate, represented by a circle.
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Welcome to digital logic circuits analysis! Today we'll solve truth tables for two combinational logic circuits. Digital circuits process binary inputs - zeros and ones - to produce binary outputs. Truth tables systematically show all possible input combinations and their corresponding outputs. Let's start by understanding the basic logic gates we'll encounter.
Now let's analyze Circuit 1 in detail. This circuit has two inputs A and B, which pass through buffers labeled '1' to create signals C and D. The key insight is that C equals A and D equals B. The circuit uses two AND gates and one OR gate. The top AND gate takes input A and the inverted signal from D, which is NOT B. The bottom AND gate takes input B and the inverted signal from C, which is NOT A. The OR gate combines these outputs. This creates the XOR function: F equals A XOR B.
Let's construct the truth table for Circuit 1. We evaluate all possible input combinations. When A equals 0 and B equals 0, both AND gates output 0, so F equals 0. When A equals 0 and B equals 1, the bottom AND gate outputs 1, so F equals 1. When A equals 1 and B equals 0, the top AND gate outputs 1, so F equals 1. When A equals 1 and B equals 1, both AND gates output 0, so F equals 0. This confirms that Circuit 1 implements the XOR function, where the output is 1 only when inputs are different.
Now let's analyze Circuit 2, which reveals an interesting logical contradiction. Input A connects directly to point C, so C equals A. The top AND gate receives input A and the inverted signal from C. Since C equals A, this becomes A AND NOT A, which is always 0 regardless of A's value. The bottom AND gate receives C and B, which equals A AND B. The final AND gate combines these outputs: 0 AND the result of A AND B. Since anything AND with 0 equals 0, the final output F is always 0, making this circuit functionally useless.
Let's complete the truth table for Circuit 2. For all input combinations - 0,0 - 0,1 - 1,0 - and 1,1 - the output F is always 0. This confirms our analysis that the logical contradiction makes this circuit output constant zero. In summary, we've analyzed two very different circuits: Circuit 1 implements the useful XOR function, outputting 1 when inputs differ. Circuit 2 demonstrates how logical contradictions can render a circuit useless, always outputting 0. This assignment shows the importance of careful logic design in digital systems.