Convert each of the following to their respective Decimal, Octal, Hexadecimal and binary representation: (a) (742)8 (b) (1011)2 (c) (47)10 (d) (3EAC)16

(a)

(b)

(c)

(d)

Explanation:

(a) (742)8 to decimal.

By expansion,

(742)8 = 7 x + 4 x + 2 x

           = 7 x 64 + 4 x 8 + 2 x 1

           = 482

∴ (742)8 =

(b) (1011)2 to octal.

By expansion,

(1011)2 = 1 x + 0 x + 1 x 2 + 1 x

           = 8 + 0 + 2 + 1

           = 11

Converting 11 to octal, divide by 8 continuously and note the remainders in the process.

11 =

∴ (1011)2 =

(c) (47)10 to hexadecimal.

Divide (47)10 by 16 continuously and note the remainders in the process.

(47)10 =

(d) (3EAC)16 to binary.

By expansion,

(3EAC)16 = 3 x + 14 x + 10 x 16 + 12 x

               = 12288 + 3584 + 160 + 12

               = 16044

Converting 16044 to binary, divide continuously by 2 and note the remainders in the process.

(3EAC)16 =