Combinational Logic

Wire

Connect a one-bit input directly to an output.

2-to-1 Multiplexer (Gate-Level)

Build a 2-to-1 multiplexer using only basic AND/OR/NOT gates instead of a behavioral assign statement.

Ground

Drive an output permanently low.

4-to-1 Multiplexer

Select one of four single-bit inputs with a 2-bit select signal.

BCD to 7-Segment Display Decoder

Decode a 4-bit BCD digit into the seven segment-drive signals of a 7-segment display.

NOR

Implement a two-input NOR gate.

Another Gate

Implement the two-input AND gate with the second input inverted.

4-bit Priority Encoder

Report the bit position of the highest set bit in a 4-bit input, with a valid flag for all-zero input.

Karnaugh Map Function

Implement the four-variable function from the Karnaugh map. Inputs are `x(4 downto 1)`, with columns labeled `x1x2` and rows labeled `x3x4`.

Two Gates

Cascade an XNOR gate and an XOR gate as shown.

8-bit Magnitude Comparator

Compare two 8-bit unsigned values and report equal, greater-than, and less-than as three one-hot flags.

More Logic Gates

Build independent NAND and NOR outputs.

7420 Chip

Model two independent four-input NAND gates.

4-bit Barrel Shifter (Rotate Left)

Rotate a 4-bit value left by a variable amount using a combinational barrel shifter.

Two-Bit Equality

Compare two two-bit values for equality.

Simple Circuit A

Implement a three-input function with an OR stage feeding an AND stage.

Simple Circuit B

Implement a sum-of-products Boolean function.

Combine Two Circuits

Combine two independently computed Boolean terms.

Ring or Vibrate?

Choose whether a phone rings or vibrates when a call arrives.

Thermostat

Drive heater and cooler controls from temperature and enable signals.

3-Bit Population Count

Count the one bits in a three-bit input.

2-to-1 Bus Multiplexer

Select one of two eight-bit buses.

9-to-1 Multiplexer

Select one of nine bits with a four-bit selector.

256-to-1 Multiplexer

Select one bit from a 256-bit input using an eight-bit index.

256-to-1 4-Bit Multiplexer

Select one four-bit word from 256 packed choices.

3-Bit Binary Adder

Add two three-bit unsigned numbers and expose the carry bit.

32-Bit Adder

Add two 32-bit unsigned operands with a carry-preserving result.

Signed Addition Overflow

Add signed bytes and flag when the mathematical result exceeds the signed range.

100-Bit Binary Adder

Add two 100-bit operands and preserve the final carry.

4-Digit BCD Adder

Add two four-digit packed BCD values with decimal carry propagation.

3-Variable Karnaugh Map

Implement the three-variable Boolean function shown by the K-map. The columns are input `a`; the rows are `bc` in Gray-code order.

4-Variable Karnaugh Map 1

Implement the four-variable function shown by the original Karnaugh map. Columns are `ab = 00, 01, 11, 10`; rows are `cd = 00, 01, 11, 10`.

4-Variable Karnaugh Map 2

Implement the four-variable function shown by the Karnaugh map. The `d` cells are don’t-cares and may be treated as either 0 or 1 to simplify the circuit.

4-Variable Karnaugh Map 3

Implement the four-variable function in the K-map. Changing any single input bit must invert the output.

Minimum SOP and POS Forms

Express a Boolean function in equivalent minimized SOP and POS forms.

K-map Function Using Multiplexers

Build the four data inputs for the supplied 4-to-1 mux using only 2-to-1 muxes. The mux uses `a` and `b` as its select inputs; this module receives only `c` and `d` and returns `mux_in[3:0]`.

Truth Tables

Translate two three-input truth tables into combinational logic.

Even Longer Vectors

Apply a bitwise operation across two 64-bit buses.

Karnaugh Map with Don’t-Cares

Minimize a four-variable Boolean function using the supplied K-map. The cells marked `d` are don’t-cares.