Answer:
(a) [tex]482_{10}[/tex]
(b) [tex]13_{8}[/tex]
(c) [tex]2B_{16}[/tex]
(d) [tex]11111010101100_{2}[/tex]
Explanation:
(a) (742)8 to decimal.
By expansion,
(742)8 = 7 x [tex]8^{2}[/tex] + 4 x [tex]8^{1}[/tex] + 2 x [tex]8^{0}[/tex]
= 7 x 64 + 4 x 8 + 2 x 1
= 482
∴ (742)8 = [tex]482_{10}[/tex]
(b) (1011)2 to octal.
By expansion,
(1011)2 = 1 x [tex]2^{3}[/tex] + 0 x [tex]2^{2}[/tex] + 1 x 2 + 1 x [tex]2^{0}[/tex]
= 8 + 0 + 2 + 1
= 11
Converting 11 to octal, divide by 8 continuously and note the remainders in the process.
11 = [tex]13_{8}[/tex]
∴ (1011)2 = [tex]13_{8}[/tex]
(c) (47)10 to hexadecimal.
Divide (47)10 by 16 continuously and note the remainders in the process.
(47)10 = [tex]2B_{16}[/tex]
(d) (3EAC)16 to binary.
By expansion,
(3EAC)16 = 3 x [tex]16^{3}[/tex] + 14 x [tex]16^{2}[/tex] + 10 x 16 + 12 x [tex]16^{0}[/tex]
= 12288 + 3584 + 160 + 12
= 16044
Converting 16044 to binary, divide continuously by 2 and note the remainders in the process.
(3EAC)16 = [tex]11111010101100_{2}[/tex]
