Chapter 02: Combinational Logic

What is Combinational Logic?

Combinational logic means the output depends ONLY on the current inputs. No memory, no history, no state. Change the inputs, output changes instantly (within nanoseconds).

All Basic Logic Gates

Gate	Operator	Function	Example
AND	&	Both inputs HIGH	y = a & b;
OR	|	At least one HIGH	y = a | b;
NOT	~	Invert signal	y = ~a;
XOR	^	Inputs different	y = a ^ b;
NAND	~(&)	NOT AND	y = ~(a & b);
NOR	~(|)	NOT OR	y = ~(a | b);

Building a 4-Input Logic Function

Let's build something useful: A 2-to-4 decoder. Takes 2 input bits, activates one of 4 outputs.

Truth Table

A  B  |  Y0  Y1  Y2  Y3
------+----------------
0  0  |   1   0   0   0
0  1  |   0   1   0   0
1  0  |   0   0   1   0
1  1  |   0   0   0   1

The Verilog

// 2-to-4 Decoder
// Only ONE output is HIGH based on input combination

module decoder_2to4 (
    input  a,
    input  b,
    output y0,
    output y1,
    output y2,
    output y3
);

    // Each output is HIGH for ONE specific input combination
    assign y0 = ~a & ~b;  // 00
    assign y1 = ~a &  b;  // 01
    assign y2 =  a & ~b;  // 10
    assign y3 =  a &  b;  // 11

endmodule

Multi-bit Signals (Buses)

Instead of declaring many single wires, use buses - multi-bit signals:

// Same decoder, cleaner code using buses

module decoder_2to4_bus (
    input  [1:0] sel,      // 2-bit input bus
    output [3:0] y         // 4-bit output bus
);

    // Use shift operator to activate the correct bit
    assign y = 4'b0001 << sel;

endmodule

Multiplexer (MUX): The Universal Selector

A multiplexer selects ONE input from many to pass to the output. It's like a railroad switch.

// 4-to-1 Multiplexer
// Select which of 4 inputs appears at output

module mux_4to1 (
    input  [3:0] data_in,     // 4 data inputs
    input  [1:0] sel,          // 2-bit selector
    output       data_out      // Selected output
);

    // Use selector to index into the data bus
    assign data_out = data_in[sel];

endmodule

Real Example: 8-bit Adder

// Add two 8-bit numbers

module adder_8bit (
    input  [7:0] a,
    input  [7:0] b,
    output [7:0] sum,
    output       carry_out
);

    // Add with carry capture
    // {carry_out, sum} creates a 9-bit result
    assign {carry_out, sum} = a + b;

endmodule

Exercise: Build an ALU

Create an Arithmetic Logic Unit that can ADD, SUB, AND, OR based on operation select:

module alu_4bit (
    input  [3:0] a, b,
    input  [1:0] op,       // 00=ADD, 01=SUB, 10=AND, 11=OR
    output reg [3:0] result
);

    always @(*) begin
        case(op)
            2'b00: result = a + b;
            2'b01: result = a - b;
            2'b10: result = a & b;
            2'b11: result = a | b;
        endcase
    end

endmodule

Key Takeaways

• Combinational logic has NO memory - output = f(current inputs)
• Use buses [N:0] for multi-bit signals
• Operators (+, -, &, |, ^, ~, <<, >>) synthesize to real gates
• assign for simple connections, always @(*) for complex logic
• Hardware executes ALL paths simultaneously (not sequential like software!)