Question

Simplify the following expression by means of a four-variable K−Map, to a minimum number of terms and factors. - ABC+CD+B

C
ˉ
D+
B
ˉ
C, with don't care condition: x=
A
ˉ
BC
D
ˉ

Answer 1

The given expression can be simplified using a four-variable K-Map by finding the largest groups of 1s and combining them into simplified terms.

Step-by-step explanation:

The given expression: \( -ABC + CD + \bar{B}C D + \bar{BC} \) with don't care conditions: \( x = \bar{A}BC\bar{D} \) can be simplified using a four-variable K-Map.

First, construct the K-Map using the variables A, B, C, and D. Fill in the values for the given expression, taking into account the don't care condition:

\( C'D' \) | \( C'D \) | \( CD \) | \( CD' \) |
\( AB\bar{C}\bar{D} \) | 0 | 1 | 1 | x |
\( AB\bar{C}D \) | 1 | 0 | 1 | x |
\( A\bar{B}CD \) | 1 | 1 | 1 | 0 |
\( A\bar{B}C\bar{D} \) | x | x | x | 0 |

Next, find the largest groups of 1s in the K-Map. Combine those groups into simplified terms. In this case, there is one group of 1s that can be combined: \( CD + \bar{B}C \).

The simplified expression is: \( -ABC + CD + \bar{B}C \).

Learn more about Simplifying expressions