optimise and simplify these expressions:

$\text{'}$ means NOT

Segment a:$$

A$$B$$C$$D$+$ A$$B$$CD$+$ A$$B$$CD$+$ A$$BC$$D $+$ A$$BCD$+$ A$$BCD $+$ AB$$C$$D$+$ AB$$C$$D $+$ AB$$CD$+$ABC$$D$+$ ABCD$+$ ABCD

Segment b:$$

A$$B$$C$$D$+$ A$$B$$C$$D $+$ A$$B$$CD$+$ A$$B$$CD $+$ A$$BC$$D$+$ A$$BCD $+$ AB$$C$$D$+$ AB$$C$$D $+$ AB$$CD$+$ ABC$$D$$

Segment c:$$

$$A$$B$$C$$D$+$ A$$B$$C$$D $+$ A$$B$$CD $+$ A$$BC$$D$+$A$$BC$$D $+$ A$$BCD$+$ A$$BCD $+$ AB$$C$$D$+$ AB$$C$$D $+$ AB$$CD$+$ AB$$CD $+$ ABC$$D$$

Segment d:$$

A$$B$$C$$D$+$ A$$B$$CD$+$ A$$B$$CD $+$ A$$BC$$D $+$ A$$BCD$+$ AB$$C$$D$+$ AB$$C$$D $+$ AB$$CD $+$ ABC$$D$+$ ABC$$D $+$ ABCD$$

Segment e:$$

A$$B$$C$$D$+$ A$$B$$CD$+$ A$$BCD$+$ AB$$C$$D$+$ AB$$CD$+$ AB$$CD $+$ ABC$$D$+$ ABC$$D $+$ ABCD$+$ ABCD

Segment f:$$

A$$B$$C$$D$+$ A$$BC$$D$+$ A$$BC$$D $+$ A$$BCD$+$ AB$$C$$D$+$ AB$$C$$D $+$ AB$$CD$+$ AB$$CD $+$ ABC$$D$+$ ABCD$+$ ABCD

Segment g:$$

A$$B$$CD$+$ A$$B$$CD $+$ A$$BC$$D$+$ A$$BC$$D $+$ A$$BCD$+$ AB$$C$$D$+$ AB$$C$$D $+$ AB$$CD$+$ AB$$CD $+$ ABC$$D $+$ ABCD$+$ ABCD