Building Blocks of Digital Systems
In Computer Organization & Architecture (COA), we deal with how computers are built at the hardware level.
At the lowest level, everything is 0s and 1s (binary signals).
To process these signals, we need logic circuits.
🔹 Combinational Circuits – Output depends only on current inputs.
🔹 Sequential Circuits – Output depends on current + past inputs (memory).
A combinational circuit is a digital circuit where the output is purely a function of the inputs at that moment.
No storage of past values.
No clock signals needed.
Think of it like a calculator: you give inputs → instantly you get output.
Output does not go back into the input.
Each calculation is fresh, independent of history.
Same inputs → always same outputs.
Example: In a Half Adder, 1 + 1 will always give Sum = 0, Carry = 1.
Built using AND, OR, NOT, NAND, NOR, XOR gates.
Boolean expressions help in simplifying and designing circuits.
Works like a digital switch.
Selects one of many inputs → sends it to output based on a control signal.
Example: A 4-to-1 MUX has 4 inputs (I0, I1, I2, I3), but only one goes to output depending on the 2-bit select line (S1, S0).
➝ Used in CPUs for data routing (choosing between instruction/data sources).
Does the opposite of MUX.
Takes an n-bit input → activates exactly one of the 2^n outputs.
Example: A 3-to-8 decoder:
Input = 011 (3 in decimal) → Output line 3 goes HIGH, others LOW.
➝ Used in memory address decoding (selecting which memory location to access).
Performs binary addition.
Half Adder: Adds 2 bits → gives Sum + Carry.
Full Adder: Adds 3 bits (A, B, Carry-in) → gives Sum + Carry-out.
➝ Used in Arithmetic Logic Unit (ALU) of processors.
Opposite of Decoder.
Converts multiple input signals → single binary code output.
Example: A 4-to-2 Encoder:
If input line D3 = 1, output = 11 (binary for 3).
➝ Used in data compression, error detection.
Output changes instantly with input.
No need to wait for clock cycles (unlike sequential circuits).
Easier to design and analyze.
Just need truth tables and Boolean algebra.
Found everywhere in computers:
✅ In simple words:
Combinational circuits are the instant decision-makers in computers.
They do not remember past inputs. Their job is to quickly compute results (arithmetic, routing, logic) so that bigger systems like processors and memory can work efficiently.