Question

1 convert (101011)2 ( )10 ? convert(596)10= ( )16 ? convert( 101011101)2 ( )16 ? convert(37)10= ( )2 ?​

Answer 1

Question:

(a) convert (101011)₂ = ( )₁₀ ?

(b) convert(596)₁₀= ( )₁₆ ?

(c) convert( 101011101)₂ = ( )₁₆ ?

(d) convert(37)₁₀= ( )₂ ?​

Answer:

(a) (101011)₂ = ( 43)₁₀

(b) (596)₁₀= ( 254)₁₆

(c) ( 101011101)₂ = ( 15D)₁₆

(d) (37)₁₀= ( 100101)₂

Explanation:

(a) convert (101011)₂ = ( )₁₀

This means that (101011)₂ be converted to base 10 (decimal).

To convert from binary to decimal, find the sum of the binary digits times their power of 2. i.e

(101011)₂ = 1 x 2⁵ + 0 x 2⁴ + 1 x 2³ + 0 x 2² + 1 x 2¹ + 1 x 2⁰

(101011)₂ = 1 x 32 + 0 x 16 + 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1

(101011)₂ = 32 + 0 + 8 + 0 + 2 + 1

(101011)₂ = 43₁₀

Therefore, (101011)₂ = ( 43)₁₀

(b) convert(596)₁₀= ( )₁₆

This means that (596)₁₀ be converted to base 16 (hexadecimal).

To convert from decimal to hexadecimal,

i. start by dividing the decimal number by 16 taking note of the result and the remainder.

ii. divide the result obtained in (i) by 16 and take note of the new result and the remainder.

iii. repeat steps i and ii until the result is 0.

iv. the result is a combination of the remainders starting from the last.

16 | 596

16 | 37 r 4

16 | 2 r 5

    | 0 r 2

Now combine the remainders starting from the bottom up. i.e

254₁₆

Therefore, (596)₁₀= ( 254)₁₆

(c) convert ( 101011101)₂ = ( )₁₆

This means that (101011101)₂ be converted to base 16 (hexadecimal).

To convert from binary to hexadecimal,

i. starting from the rightmost bit, group the binary digits into a group of 4 bits as follows

101011101 => 1   0101    1101

ii. the group that does not contain 4 bits is padded with 0s

101011101 => 0001   0101    1101

iii. using the hexadecimal table, convert each group to hexadecimal as follows.

0001 = 1

0101 = 5

1101 = D

iv. combine the result

15D

Therefore, ( 101011101)₂ = ( 15D)₁₆

(d)  convert(37)₁₀= ( )₂

This means that (37)₁₀ be converted to base 2 (binary).

To convert from decimal to binary,

i. start by dividing the decimal number by 2 taking note of the result and the remainder.

ii. divide the result obtained in (i) by 2 and take note of the new result and the remainder.

iii. repeat steps i and ii until the result is 0.

iv. the result is a combination of the remainders starting from the last.

2 | 37

2 | 18 r 1

2 | 9 r 0

2 | 4 r 1

2 | 2 r 0

2 | 1 r 0

  | 0 r 1

Now combine the remainders starting from the bottom up. i.e

100101₂

Therefore, (37)₁₀= ( 100101)₂