Simplify with K-Maps

CSC-116 · Semester I · Digital Logic

intermediate25 minAvailable

Live simulation14 components · 15 wires

OFF

NOT

B'C'

B'D'

A'C'

Click a switch to toggle it · drag output → input to wire · drag to move · Delete removes the selection · Ctrl+Z undoes.

Truth table

live from the current circuit

A	B	C	D	F
0	0	0	0	1
0	0	0	1	1
0	0	1	0	1
0	0	1	1	0
0	1	0	0	1
0	1	0	1	1
0	1	1	0	0
0	1	1	1	0
1	0	0	0	1
1	0	0	1	1
1	0	1	0	1
1	0	1	1	0
1	1	0	0	0
1	1	0	1	0
1	1	1	0	0
1	1	1	1	0

Lab brief

Objective

Simplify a 4-variable Boolean function with a Karnaugh map, then implement and verify the minimized circuit.

Theory & concepts

A K-map arranges the truth table so adjacent cells differ in one variable. Grouping 1s in powers-of-two rectangles lets variables cancel. For F = AB'C' + A'BC + ABC + AB'C, grouping adjacent 1s removes the cancelling variable from each pair.

Rendering diagram…

K-map simplification workflow

Check the count: the unsimplified sum-of-minterms needs eight 4-input AND terms; the minimized version needs only three 2-input terms.

Prerequisites

Lesson: Karnaugh maps
Lesson: Four-variable K-maps

Instructions

1Draw the 4-variable K-map for the given minterm list and place a 1 in each cell.
2Circle the largest legal power-of-two groups (wrap-around allowed).
3Write the product term for each group: keep only variables constant across the group.
4Wire AND gates for each product term and OR them into the output LED.
5Test several input combinations, including at least one per group.

Tasks

Map the minterms
Fill in the K-map grid for the given Σm list.
Group and simplify
Circle groups and write the minimized SOP expression.
Compare gate counts
Count gates for the canonical vs minimized implementation and explain the saving.

Self-check

The K-map is filled correctly and groups are maximal powers of two.
The minimized expression is equivalent to the original function.
The implemented circuit produces the correct output on sampled inputs.

Environment

gate palettewire connectionslive simulationtruth table check

A	B	C	D	F
0	0	0	0	1
0	0	0	1	1
0	0	1	0	1
0	0	1	1	0
0	1	0	0	1
0	1	0	1	1
0	1	1	0	0
0	1	1	1	0
1	0	0	0	1
1	0	0	1	1
1	0	1	0	1
1	0	1	1	0
1	1	0	0	0
1	1	0	1	0
1	1	1	0	0
1	1	1	1	0

A	B	C	D	F
0	0	0	0	1
0	0	0	1	1
0	0	1	0	1
0	0	1	1	0
0	1	0	0	1
0	1	0	1	1
0	1	1	0	0
0	1	1	1	0
1	0	0	0	1
1	0	0	1	1
1	0	1	0	1
1	0	1	1	0
1	1	0	0	0
1	1	0	1	0
1	1	1	0	0
1	1	1	1	0

A	B	C	D	F
0	0	0	0	1
0	0	0	1	1
0	0	1	0	1
0	0	1	1	0
0	1	0	0	1
0	1	0	1	1
0	1	1	0	0
0	1	1	1	0
1	0	0	0	1
1	0	0	1	1
1	0	1	0	1
1	0	1	1	0
1	1	0	0	0
1	1	0	1	0
1	1	1	0	0
1	1	1	1	0