Determine the hybridization of the carbon atoms in the following compounds:
$(a)$ $N \equiv C-CH=CH_2$
$(b)$ $HC \equiv C-CH=CH_2$ (Identify the carbon atoms of the single bond $C-C$)
$(c)$ $HC \equiv C-C \equiv CH$
$(d)$ $H_2C=C=C=CH_2$
$(e)$ Buta$-1,3-$diene (as shown in the figure)

(N/A) In $N \equiv C-CH=CH_2$,the carbon atoms are $sp, sp^2, sp^2$ hybridized respectively.
$(b)$ In $HC \equiv C-CH=CH_2$,the carbon atoms involved in the single bond $C-C$ are $sp$ and $sp^2$ hybridized.
$(c)$ In $HC \equiv C-C \equiv CH$,all four carbon atoms are $sp$ hybridized.
$(d)$ In $H_2C=C=C=CH_2$,the terminal carbons are $sp^2$ hybridized and the two central carbons are $sp$ hybridized.
$(e)$ In buta$-1,3-$diene $(CH_2=CH-CH=CH_2)$,all four carbon atoms are $sp^2$ hybridized.