We have to convert (AB)16  into its BCD and Octal equivalent.

(1) (AB)16 into BCD

1.Convert given hexadecimal number into Decimal equivalent

(AB)16 =  (1010 1011)2       .... (*)

$(1010 1011)_2 = ((1\times128)+(0\times64)+(1\times32)+(0\times16)+(1\times8)+(0\times4)+(1\times2)+(1\times 1))=(173)10$

2.Convert the evaluated decimal equivalent into BCD code

$(173)_{10} = (0001 0111 0011) = (000101110011)_{BCD}$

(2) (AB)16 into Octal

From conversion equation (*),we got

(AB)16 =  (1010 1011)2 

Now to convert to octal,simply group the numbers in groups of 3 digits from LSB and convert into equivalent octal code

Thus,$(AB)_{16} = (1010 1011)_2 = (010 101 011) = (2 \ 5\ 3)_8$

Thus, (AB)16 = (000101110011)BCD

(AB)16 = (253)8