explain

Using a Karnaugh map, convert the following standard POS expression into a minimum POS expression, a standard SOP expression, and a minimum SOP expression. ( A + B + C + D ) ( A + B + C + D) ( A + B + C + Dj ( A + B + C + D) (A + B + C + D)(A + B + C+ D) Solution The Os for the standard POS expression are mapped and grouped to obtain the minimum POS expression in Figure 4-47(a). In Figure 4-47(b), Is are added to the cells that do not contain Os. From each cell containing a 1, a standard product term is obtained as indicated. These product terms form the standard SOP expression. In Figure 4-47(c), the Is are grouped and a minimum SOP expression is obtained. A +B +C ABCD ABCD 00 CD 11 10 AP 00 11/ 10 ABCD ABCD B +C+D ABCD 10 10 ABCD B +C+D ABCD ABCD ABCD ABCD (a) Minimum POS: (A + 8 + CXB + C + DXB + C + D) (b) Standard SOP: ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD AR 00 11/ 10 BC 11 10 AC BCD (c) Minimum SOP: AC + BC + BD + BCD