A) Design a Full Adder
A full adder is a digital circuit that adds three binary digits (bits) and produces a sum and carry output.
Requirements:
- Three input bits: A, B, and Cin (carry-in)
- Two output bits: Sum (S) and Cout (carry-out)
Truth Table:
Circuit Design:
We'll use logic gates and our previously designed half adder to implement the full adder.
Circuit Diagram:
(Half Adder 1)
A ---XOR--> S1
B ---XOR--> S1
A ---AND--> C1
B ---AND--> C1
A ---XOR--> S1
B ---XOR--> S1
A ---AND--> C1
B ---AND--> C1
(Half Adder 2)
S1 ---XOR--> S
Cin ---XOR--> S
C1 ---AND--> Cout
Cin ---AND--> Cout
S1 ---XOR--> S
Cin ---XOR--> S
C1 ---AND--> Cout
Cin ---AND--> Cout
How it works:
- The first half adder produces a sum (S1) and carry (C1).
- The second half adder adds S1, Cin, and produces the final sum (S) and carry (Cout).
Let's simulate the full adder with different input combinations to ensure it works correctly!
Once you're ready, we can move on to...
B) Explore other digital circuits (e.g., subtractor, multiplier) B) Explore other digital circuits
Now that we have a solid understanding of adders, let's explore other digital circuits:
1. Subtractor:
A subtractor is a digital circuit that subtracts two binary numbers.
Requirements:
- Two input bits: A (minuend) and B (subtrahend)
- Two output bits: Difference (D) and Borrow (B)
Circuit Design:
We can use a similar approach to the adder, but with some modifications.
2. Multiplier:
A multiplier is a digital circuit that multiplies two binary numbers.
Requirements:
- Two input bits: A and B
- Four output bits: Product (P)
Circuit Design:
We can use a combination of AND gates and adders to implement the multiplier.
Other Digital Circuits:
- Encoder: Converts decimal to binary
- Decoder: Converts binary to decimal
- Multiplexer: Selects one of many inputs
- Demultiplexer: Distributes an input to many outputs
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