Binary - Decimal Conversion Practice PDF

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School of Business, Economics and Informatics

Binary – Decimal Conversion Practice A) Convert the following binary numbers into decimal numbers: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

1010100 1010 110011 101111 1000111 1010101010 10010010 10101 111111 1110001

B) Convert the following decimal numbers into binary numbers:

B) 1) 10001 2) 100000000 3) 100010 4) 1111 5) 110110 6) 1111011 7) 1001100 8) 100010110 9) 1000011 10) 10110

17 256 34 15 54 123 76 278 67 22

Answers: A) 1) 84 2) 10 3) 51 4) 47 5) 71 6) 682 7) 146 8) 21 9) 63 10) 113

1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

You can find detailed answers on the following two pages. [email protected]

Page 1

School of Business, Economics and Informatics

Binary – Decimal Conversion Practice Answers Explained A) Convert the following binary numbers into decimal numbers: Use the binary place value table to help with the conversion. When placing the binary number in the table start from the smallest place value, which is the right most digit (see below). Only concentrate on the non 0 terms and simply add their place values together:

29 28 27 26 512 256 128 64 1

1) 2) 3) 4) 5) 6) 1 7) 8) 9) 10)

0

1 1

25 24 32 16 0 1

1 0 0

1 1 0 1 0

1

1 1

1 0 0 0 1 1 1 1

23 8 0 1 0 1 0 1 0 0 1 0

22 4 1 0 0 1 1 0 0 1 1 0

21 2 0 1 1 1 1 1 1 0 1 0

20 1 0 0 1 1 1 0 0 1 1 1

1) 64 + 16 + 4 = 84

2) 8 + 2 = 10

3) 32 + 16 + 2 + 1 = 51

4) 32 + 8 + 4 + 2 + 1 = 47

5) 64 + 4 + 2 + 1 = 71

6) 512 + 128 + 32 + 8 + 2 = 682

7) 128 + 16 + 2 = 146

8) 16 + 4 + 1 = 21

9) 32 + 16 + 8 + 4 + 2 + 1 = 63

10) 64 + 32 + 16 + 1 = 113

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Page 2

School of Business, Economics and Informatics B) Convert the following decimal numbers into binary numbers: When converting decimal numbers to binary numbers; look for the place values which can be added together to make the decimal number. You can also think about it as subtracting the highest power of 2 from the number, find the remainder and repeat till the remainder is 1 or 0. Place a 1 at every place value used and a 0 to all that was not used. The binary place value table is a very handy visual aid here:

28 27 26 256 128 64 1) 17 2) 256 3) 34 4) 15 5) 54 6) 123 7) 76 8) 278 9) 67 10) 22

1

1

0

0

0

1 1 0 1

25 24 32 16 1 0 0 1 0 1 1 0 0 0

1 1 0 1 0 1

23 8 0 0 0 1 0 1 1 0 0 0

22 4 0 0 0 1 1 0 1 1 0 1

21 2 0 0 1 1 1 1 0 1 1 1

20 1 1 0 0 1 0 1 0 0 1 0

1) 17 = 16 +1

2) 256

3) 34 = 32 + 2

4) 15 = 8 + 4 + 2 + 1

5) 54 = 32 + 16 + 4 + 2

6) 123 = 64 + 32 + 16 + 8 + 2 + 1

7) 76 = 64 + 8 + 4

8) 278 = 256 + 16 + 4 + 2

9) 67 = 64 + 2 + 1

10) 22 = 16 + 4 + 2

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