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

Three-Variable K-Map: Identify Prime Implicants and Essential Prime Implicants

MediumLogic CircuitAnalyze

Logic synthesis tools rely on exact minimization algorithms to reduce transistor count and propagation delay before physical layout.

The three-variable Karnaugh map below defines a Boolean function F over inputs A, B, and C.

| A \ BC | 00 | 01 | 11 | 10 | |---|---|---|---|---| | 0 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 1 | 0 |

Identify all prime implicants and essential prime implicants. Determine the minimal sum-of-products expression for F.

Constraints

  • Assume standard minterm indexing where A is the most significant bit and C is the least significant bit.
  • A prime implicant is the largest possible grouping of 1s that cannot be entirely consumed by a larger valid group.
  • An essential prime implicant contains at least one minterm that is not covered by any other prime implicant.

Topics

optimizationboolean-algebraprime-implicantsk-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