Combinational Circuits

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Arjit Sharma
01 Min

Combinational circuits are circuits without memory. Their output depends only on the current input values and not on any previous state.

Key Characteristics -

  • No feedback or storage elements
  • Outputs change instantly with input changes
  • Defined by Boolean expressions or truth tables

Types of Combinational Circuits

1. Adder

Add binary numbers.

  • Half Adder: Adds two 1-bit inputs (A, B)
    • Outputs: Sum = A ⊕ B, Carry = A·B half-adder
  • Full Adder: Adds three 1-bit inputs (A, B, Carry-in)
    • Outputs: Sum and Carry-out
    • Built using two half adders and an OR gate

2. Subtractor

Subtract binary numbers.

  • Half Subtractor: Subtracts B from A (A-B)
    • Outputs: Diff = A ⊕ B, Borrow = ¬A · B half-subtractor
  • Full Subtractor: Subtracts with a borrow (A – B – Borrow-in)
    • Outputs: Difference and Borrow-out

3. Multiplexer (MUX)

Acts like a switch to pick one input to send to the output.

  • 2-to-1 MUX:
    • Inputs: A, B; Select: S
    • Output: Y = A·¬S + B·S Multiplexer

4. Demultiplexer (DEMUX)

Routes one input to one of many outputs based on selector bits. Its like a reverse MUX, directing data to a chosen path.

De-Multiplexer

5. Decoder

Translates n input bits into one of 2ⁿ output lines.

  • 2-to-4 decoder: Inputs: 2 bits → Outputs: 4 lines, with only one active at a time

6. Encoder

Converts one of 2ⁿ active inputs into an n-bit binary code. Opposite of a decoder; only one input should be active at a time.

Conclusion

These components are the building blocks of more advanced hardware systems like ALUs, control units, and memory addressing circuits.

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