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Note: You can use a word document to write your answers and copy-paste your answer to the area specified. a. (5 points) Convert the following base 16 numbers to base 10. Show your calculation steps. EA916 CB216 b. (5 points) Convert the following binary numbers to base 10. Show your calculation steps. (The space between numbers is left to make the reading easy.) (1011 1110 1101 1011 1010)2 (1010 1000 1011 1000 1110 1101)2 c. (5 points) Convert the following binary numbers to base 16. Show your calculation steps. i. (1011 1110 1101 1011 1010)2 ii. (1010 1000 1011 1000 1110 1101)2 d. (5 points) Convert the following decimal number to octal. i. 74510 ii. 67210

User Neeta
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1 Answer

18 votes
18 votes

Answer:


EA9_(16) = 3753


CB2_(16) = 3250


(1011 1110 1101 1011 1010)_2 = 781754


(1010 1000 1011 1000 1110 1101)_2 = 11057389


(1011 1110 1101 1011 1010)_2 = BEDBA


(1010 1000 1011 1000 1110 1101)_2 = A8B8ED


74510_8= 221416


67210_8 = 203212

Step-by-step explanation:

Solving (a): To base 10


(i)\ EA9_{16

We simply multiply each digit by a base of 16 to the power of their position.

i.e.


EA9_(16) = E * 16^2 + A * 16^1 + 9 * 16^0


EA9_(16) = E * 256 + A * 16 + 9 * 1

In hexadecimal


A = 10; E = 14

So:


EA9_(16) = 14 * 256 + 10 * 16 + 9 * 1


EA9_(16) = 3753


(ii)\ CB2_(16)

This gives:


CB2_(16) = C * 16^2 + B * 16^1 + 2 * 16^0


CB2_(16) = C * 256 + B * 16 + 2 * 1

In hexadecimal


C = 12; B =11

So:


CB2_(16) = 12 * 256 + 11 * 16 + 2 * 1


CB2_(16) = 3250

Solving (b): To base 10


(i)\ (1011 1110 1101 1011 1010)_2

We simply multiply each digit by a base of 2 to the power of their position.

i.e.


(1011 1110 1101 1011 1010)_2 = 1 * 2^(19) + 0 * 2^(18) + 1 * 2^(17) + 1 * 2^(16) +1 * 2^(15) + 1 * 2^(14) + 1 * 2^(13) + 0 * 2^(12) + 1 * 2^(11) + 1 * 2^(10) + 0 * 2^9 + 1 * 2^8 +1 * 2^7 + 0 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0


(1011 1110 1101 1011 1010)_2 = 781754


(ii)\ (1010 1000 1011 1000 1110 1101)_2


(1010 1000 1011 1000 1110 1101)_2 = 1 * 2^(23) + 0 * 2^(22) + 1 * 2^(21) + 0 * 2^(20) +1 * 2^(19) + 0 * 2^(18) + 0 * 2^(17) + 0 * 2^(16) + 1 * 2^(15) + 0 * 2^(14) + 1 * 2^(13) + 1 * 2^(12) +1 * 2^(11) + 0 * 2^(10) + 0 * 2^9 + 0 * 2^8 + 1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 1*2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0


(1010 1000 1011 1000 1110 1101)_2 = 11057389

Solving (c): To base 16


i.\ (1011 1110 1101 1011 1010)_2

First, convert to base 10

In (b)


(1011 1110 1101 1011 1010)_2 = 781754

Next, is to divide 781754 by 16 and keep track of the remainder


781754/16\ |\ 48859\ R\ 10


48859/16\ |\ 3053\ R\ 11


3053/16\ |\ 190\ R\ 13


190/16\ |\ 11\ R\ 14


11/16\ |\ 0\ R\ 11

Write out the remainder from bottom to top


(11)(14)(13)(11)(10)

In hexadecimal


A = 10; B = 11; C = 12; D = 13; E = 14; F = 15.


(11)(14)(13)(11)(10)=BEDBA

So:


(1011 1110 1101 1011 1010)_2 = BEDBA


ii.\ (1010 1000 1011 1000 1110 1101)_2

In b


(1010 1000 1011 1000 1110 1101)_2 = 11057389

Next, is to divide 11057389 by 16 and keep track of the remainder


11057389/16\ |\ 691086\ R\ 13


691086/16\ |\ 43192\ R\ 14


43192/16\ |\ 2699\ R\ 8


2699/16\ |\ 168\ R\ 11


168/16\ |\ 10\ R\ 8


10/16\ |\ 0\ R\ 10

Write out the remainder from bottom to top


(10)8(11)8(14)(13)

In hexadecimal


A = 10; B = 11; C = 12; D = 13; E = 14; F = 15.


(10)8(11)8(14)(13) = A8B8ED

So:


(1010 1000 1011 1000 1110 1101)_2 = A8B8ED

Solving (d): To octal


(i.)\ 74510

Divide 74510 by 8 and keep track of the remainder


74510/8\ |\ 9313\ R\ 6


9313/8\ |\ 1164\ R\ 1


1164/8\ |\ 145\ R\ 4


145/8\ |\ 18\ R\ 1


18/8\ |\ 2\ R\ 2


2/8\ |\ 0\ R\ 2

Write out the remainder from bottom to top


74510_8= 221416


(ii.)\ 67210

Divide 67210 by 8 and keep track of the remainder


67210/8\ |\ 8401\ R\ 2


8401/8\ |\ 1050\ R\ 1


1050/8\ |\ 131\ R\ 2


131/8\ |\ 16\ R\ 3


16/8\ |\ 2\ R\ 0


2/8\ |\ 0\ R\ 2

Write out the remainder from bottom to top


67210_8 = 203212

User Rck
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