CodiodeCodiode
Home
Problem Solving
Skill Tracks
My Assignments
Contests
Leaderboard
Community
Settings
Codiode/Problems/Combinational Logic

Four-Variable K-Map: Checkerboard Pattern

HardLogic CircuitAnalyze

Parity generation and checking circuits rely heavily on XOR trees to detect single-bit errors in data transmission.

The Karnaugh map below represents a four-variable Boolean function Y dependent on inputs A, B, C, and D. The 1-cells are located at minterms m1, m2, m4, m7, m8, m11, m13, and m14. This configuration creates an alternating checkerboard pattern across the entire map.

Analyze the K-map for valid groupings. Determine the minimal Sum of Products expression for Y and evaluate the simplification limits of this specific topology.

Constraints

  • The K-map utilizes standard Gray code ordering: 00, 01, 11, 10 for both axes.
  • Minterms are evaluated as a standard 4-bit binary number ABCD.
  • Assume canonical Sum of Products (SOP) format is required if minimization fails.

Topics

xorboolean-algebrasimplificationk-map

Solve this problem

Place the gates, wire them up and watch the signals settle. Every submission runs on the same simulation engine that grades it.

This problem is part of Codiode Pro. The statement above is free to read.

Sign in to solveSee what Pro unlocks

The circuit builder and code editor need a desktop screen. On a phone, read the problem here and open it on a laptop to solve.

Related problems

  • Binary to HexEasy
  • 1-to-4 Demultiplexer from AND and NOT GatesEasy
  • 2-to-4 Line Decoder with Active-High EnableEasy
  • Hex Nibble to BinaryEasy
  • Odd Parity Bit Generator for 3-bit DataEasy
  • Full Adder from Half AddersEasy
  • Modulo ArithmeticMedium
  • Two's Complement: Encode a Negative DecimalEasy

Browse all problems · Learning tracks