Question

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

Answer 1

(a)
`482_(10)`

(b)
`13_(8)`

(c)
`2B_(16)`

(d)
`11111010101100_(2)`

Step-by-step explanation:

(a) (742)8 to decimal.

By expansion,

(742)8 = 7 x
`8^(2)` + 4 x
`8^(1)` + 2 x
`8^(0)`

= 7 x 64 + 4 x 8 + 2 x 1

= 482

∴ (742)8 =
`482_(10)`

(b) (1011)2 to octal.

By expansion,

(1011)2 = 1 x
`2^(3)` + 0 x
`2^(2)` + 1 x 2 + 1 x
`2^(0)`

= 8 + 0 + 2 + 1

= 11

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

11 =
`13_(8)`

∴ (1011)2 =
`13_(8)`

(c) (47)10 to hexadecimal.

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

(47)10 =
`2B_(16)`

(d) (3EAC)16 to binary.

By expansion,

(3EAC)16 = 3 x
`16^(3)` + 14 x
`16^(2)` + 10 x 16 + 12 x
`16^(0)`

= 12288 + 3584 + 160 + 12

= 16044

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

(3EAC)16 =
`11111010101100_(2)`