BINARY PRACTICE QUIZ SOLUTIONS
BASE CONVERSIONS

Convert…

Show Your Work

Answer

a)     1101 10112  to  _____ 10

 

Note: You do not need to show this many steps.  Having the chart filled in and any additions or subtractions showing is adequate.  I am showing all of these steps to make sure that you understand how to approach your solution.

 

STEP 1

We start by making the chart.  The base that is not base-10 in this problem is base-2.  So the bottom row of the chart contains powers of 2.

 

 

 

 

 

 

 

 

 

128

64

32

16

8

4

2

1

 

STEP 2

We copy the binary number into the top of the chart.  Note that both steps 1 and 2 are usually done at the same time because the chart needs to be the correct size to fit the number that we are converting.

 

1

1

0

1

1

0

1

1

128

64

32

16

8

4

2

1

 

STEP 3

We simply add up the numbers that are under the ones to get our answer.

 

128+64+16+8+2+1

=219

 

219

b)     2314  to  _____ 10

 

STEP 1

We start by making the chart.  The base that is not base-10 in this problem is base-4.  So the bottom row of the chart contains powers of 4.  Since the number that we are converting from has 3 digits, our chart only needs three columns.

 

 

 

 

16

4

1

 

STEP 2

We fill in the top row with our number to convert from.

 

2

3

1

16

4

1

 

STEP 3

So, there is a 2 in the column of 16s, 3 and in the column of 4s and 1 in the column of 1s.  Mathematically, we write this as:

 

2x16 + 3x4 + 1x1

= 32 + 12 + 1

= 45

 

45

c)     12110  to  _____ 2


STEP 1
We start with the chart.  The bottom row will contain powers of 2 because the base that is not base-10 is base 2.

 

 

 

 

 

 

 

 

 

128

64

32

16

8

4

2

1

 

STEP 2
Since this chart contains powers of two, the number in the top row has to be in base-2.  So we cannot put 121 at the top.  This is an important step to understand to be able to convert in both directions with the chart.

 

STEP 3

So this means that we have to work backwards.

 

We start by asking, how many 128s are in 121.  The answer is zero and we put that in the chart.

 

0

 

 

 

 

 

 

 

128

64

32

16

8

4

2

1

 

STEP 4

We now ask: How many 64s are in 121?  The answer is 1 and put that in the chart.

 

0

1

 

 

 

 

 

 

128

64

32

16

8

4

2

1

 

We have accounted for 64 of the 121.  So we subtract 121-64 to get 57.  We now need to continue with 57.

 

STEP 5

We now ask:  How many 32s in 57?  The answer is 1.

 

0

1

1

 

 

 

 

 

128

64

32

16

8

4

2

1

 

We now do 57-32 to get 25.

 

STEP 6

We now ask: How many 16s are in 25.  The answer is 1 and 25-16 gives us 9.

 

0

1

1

1

 

 

 

 

128

64

32

16

8

4

2

1

 

STEP 7
We now ask:  How many 8s are in 9.  The answer is 1 and 9-8 gives us 1.

 

0

1

1

1

1

 

 

 

128

64

32

16

8

4

2

1

 

STEP 8

How many 4s are in 1.  Zero.

 

How many 2s are in 1.  Zero.

 

0

1

1

1

1

0

0

 

128

64

32

16

8

4

2

1

 

STEP 9

How many 1s are in 1.  One.  That leaves us with 1 – 1 giving zero.  So we are done.

 

0

1

1

1

1

0

0

1

128

64

32

16

8

4

2

1

 

 

 

 

 

 

 

0111 1001

d)     2510  to  _____ 3

 

STEP 1

We start with the chart.  Powers of three go at the bottom.

 

 

 

 

 

27

9

3

1

 

STEP 2

We need to work backwards to find out the base 3 number that we are looking for. 

 

STEP 3

There are no 27s in 25.  So zero goes in the first column.

 

0

 

 

 

27

9

3

1

 

STEP 4

There are two 9s in 25.  So we put 2 in the second column.  After taking 9 away twice from 25, we are left with 7.

 

25 – 9 – 9 = 7

 

0

2

 

 

27

9

3

1

 

STEP 5

There are two 3s in 7.  We put 2 above in the three column.

 

7 – 3 – 3 = 1.

 

0

2

2

 

27

9

3

1


STEP 6

There is one 1 in the value 1.  So we put 1 in the last column and are left with zero.  So we are done.

 

0

2

2

1

27

9

3

1

 

 

 

 

 

 

 

221

e)     8C16  to  _____ 2

 

STEP 1

We start off by writing out the chart of binary and hex digits beside each other.

 

BIN – HEX

0000 – 0

0001 – 1

0010 – 2

0011 – 3

0100 – 4

0101 – 5

0110 – 6

0111 – 7

1000 – 8

1001 – 9

1010 – A

1011 – B

1100 – C

1101 – D

1110 – E

1111 – F

 

STEP 2

We simply replace the hex digits by the corresponding 4 binary digits.

 

8 -> 1000
C -> 1100

 

Therefore, our answer is 1000 1100.

 

 

1000 1100

f)      1001 10102  to  _____ 16

 

STEP 1

We use the same chart as in the previous problem.

 

STEP 2

1001 -> 9

1010 -> A

 

Therefore, the answer is 9A.

9A

g)     FUN36  to  ____ 10

 

STEP 1

We start with the base-36 chart.

 

 

 

 

1296

36

1

 

STEP 2

We place the number FUN inside the chart.

 

F

U

N

1296

36

1

 

STEP 3

The quiz provides a table to easily find the value of letters in base 36 (see below).

 

F -> 15
U -> 30

N -> 23

 

STEP 3

Now we simply do the scientific notation to solve our problem.

 

F x 1296 + U x 36 + N x 1

=15 x 1296 + 30 x 36 + 23 x 1

=19440 + 1080 + 23

=20543

 

 

 

 

 

 

20543

 

 

 

*** The quiz ends here. ***

Conversion chart for base 2 to/from base 10.

 

 

 

 

 

 

 

 

 

 

 

27

26

25

24

23

22

21

20

128

64

32

16

8

4

2

1

 

Blank conversion chart for any base to/from base 10.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table showing value of letters in bases 11 to 36.

A

10

H

17

O

24

V

31

B

11

I

18

P

25

W

32

C

12

J

19

Q

26

X

33

D

13

K

20

R

27

Y

34

E

14

L

21

S

28

Z

35

F

15

M

22

T

29

 

 

G

16

N

23

U

30