Question

Drag each statement to the correct location.

Answer 1

Answer:

$(a)\ 222_{10} = DE_{16}$ --- True

$(b)\ D7_{16} = 11010011_2$ --- False

$(c)\ 13_{16} = 19_{10}$ --- True

Explanation:

Required

Determine if the statements are true or not.

$(a)\ 222_{10} = DE_{16}$

To do this, we convert DE from base 16 to base 10 using product rule.

So, we have:

$DE_{16} = D * 16^1 + E * 16^0$

In hexadecimal.

$D =13 \\E = 14$

So, we have:

$DE_{16} = 13 * 16^1 + 14 * 16^0$

$DE_{16} = 222_{10}$

Hence:

(a) is true

$(b)\ D7_{16} = 11010011_2$

First, convert D7 to base 10 using product rule

$D7_{16} = D * 16^1 + 7 * 16^0$

$D = 13$

So, we have:

$D7_{16} = 13 * 16^1 + 7 * 16^0$

$D7_{16} = 215_{10}$

Next convert 215 to base 2, using division rule

$215 / 2 = 107 R 1$

$107/2 =53 R 1$

$53/2 =26 R1$

$26/2 = 13 R 0$

$13/2 = 6 R 1$

$6/2 = 3 R 0$

$3/2 = 1 R 1$

$1/2 = 0 R1$

Write the remainders from bottom to top.

$D7_{16} = 11010111_2$

Hence (b) is false

$(c)\ 13_{16} = 19_{10}$

Convert 13 to base 10 using product rule

$13_{16} = 1 * 16^1 + 3 * 16^0$

$13_{16} = 19$

Hence; (c) is true