Stevens Institute Of Technology CS 550 Chapter 3 Number Systems 1)How many binary digits does it take to represent the decimal number 2013?   16   8   11   d) 2013     How many bytes does it take to store the binary equivalent of the decimal number 1945?   1   2   4   10     The largest number that can be represented 8 bits without considering a sign is   15   b) 255   c) 65,535   d) 10,000,000     The largest single digit in octal is   1   7   8   10     The largest single digit in hexadecimal is   1   8   F   9     The binary number 101100112 is equivalent to the decimal number   a) 113   b) 179   c) 133   d) 10,110,011     Eight raised to the power zero is   0   1   8   -8     Eight raised to the power one is   0   1   8   -8     The number of different items that can be represented by a given number of digits, n, in a particular base, b, is given by the formula:                                       bn           equals  

Stevens Institute Of Technology

CS 550

Chapter 3 Number Systems

1)How many binary digits does it take to represent the decimal number 2013?

1. 1. 16

1. 2. 8

1. 3. 11

d) 2013

2. How many bytes does it take to store the binary equivalent of the decimal number 1945?

1. 1. 1

1. 2. 2

1. 3. 4

1. 4. 10

3. The largest number that can be represented 8 bits without considering a sign is

1. 1. 15

b) 255

c) 65,535

d) 10,000,000

4. The largest single digit in octal is

1. 1. 1

1. 2. 7

1. 3. 8

1. 4. 10

5. The largest single digit in hexadecimal is

1. 1. 1

1. 2. 8

1. 3. F

1. 4. 9

6. The binary number 10110011₂ is equivalent to the decimal number

a) 113

b) 179

c) 133

d) 10,110,011

7. Eight raised to the power zero is

1. 1. 0

1. 2. 1

1. 3. 8

1. 4. -8

8. Eight raised to the power one is

1. 1. 0

1. 2. 1

1. 3. 8

1. 4. -8

9. The number of different items that can be represented by a given number of digits, n, in a particular base, b, is given by the formula:                                       bn           equals   .
   1. field

1. 2. radix

1. 3. range

1. 4. parameter

10. The digit with the greatest weight (value) in a number is called the

1. radix

2. heaviest bit

3. least significant digit

4. most significant digit

11. The octal number 12₈ is equivalent to the decimal number

1. 9

2. 10

3. 24

4. 12

12. The hexadecimal number 1A₁₆ is equivalent to the decimal number

1. 9

2. 17

3. 26

d) 110

13. How many bits are there in one byte?

1. 1

2. 4

3. 8

4. 10

14. A single digit that can have only one of two values, 0 or 1, is a

1. bit

2. blip

3. signal

4. character

15. In order to divide a number by its base we can perform

1. a bit op

2. a left shift

3. a right shift

4. a complex equation

16. In order to multiply a number by its base we can perform

1. a bit op

2. a left shift

3. a right shift

4. a complex equation

17. The base 8 number system is called

1. octal

2. fractal

3. ochodecimal

4. hexadecimal

18. The base 2 number system is called

1. binary

2. fractal

3. bitly

4. radix

19. Which of the following is true? a) 1₂ <1₈

b) 10₂ < 1₈

c) 101₂ < 10₈

d) 101₂ < 5₈

20. Which of the following is true?

a) 0.1₂ > 0.1₈

b) 0.1₂ = 0.1₈

c) 0.1₂ < 0.1₈

d) None of these

21. Which of the following is true? a) 101₈ <10₁₆

b) 10₈ < 1₁₆

c) 11₈ < 10₁₆

d) 12₈ < A₁₆

22. The “Exclusive OR” function (used for the result bit when adding single digits in binary) will equal 1 if the input bits are

a) 0+0

b) 0+1

c) 1+1

d) None of these

23. The “AND” function (used for the carry bit when adding single digits in binary) will equal 1 if the input bits are a) 0+0

b) 0+1

c) 1+1

d) None of these

24. The decimal number 9 is equivalent to the hexadecimal

1. A

2. 9

3. 10

d) 1001

25. The base 16 number system is called

1. octal

2. fractal

3. sextadecimal

4. hexadecimal

26. To convert from binary to octal by grouping, one octal digit corresponds to how many binary digits?

1. one

2. two

3. three

4. eight

27. To convert from binary to hexadecimal by grouping, one hexadecimal digit corresponds to how many binary digits?

1. two

2. four

3. eight

4. sixteen

28. Ten raised to the power negative one (10^-1) is

a) 1/10

b) -10

c) -1/10

d) None of these

29. The binary number 10.01₂ is equivalent in decimal to a) 2.01

b) 2.25

c) 4.25

d) 10.01

30. The octal number 1.2₈ is equivalent in decimal to

a) 1.25

b) 8.16

c) 8.25

d) 12

31. The hexadecimal number B.4₁₆ is equivalent in decimal to a) 10.25

b) 10.5

c) 11.25

d) None of these

32. The decimal fraction ¼ (0.25) is equivalent to a) 0.1₂

b) 0.1₈

c) 0.1₁₆

d) None of these

33. The digit furthest to the right is usually the

1. radix

2. lightest bit

3. least significant digit

4. most significant digit

34. The number of different digits, including zero, that exist in the number system is the

1. range

2. field

3. base

4. parameter

35. The number point (normally known by the name of the base—for example "decimal point" in base 10)—which divides whole numbers from fractional numbers is called

1. bit point

2. radix point

3. fractal point

4. division point

Analytic questions

1. Convert this binary number 101011010₂ to Decimal.

2. Convert this binary number 101011010₂ to Octal.

3. Convert this binary number 101011010₂ to Hexadecimal.

4. Show the decimal number 147 in Binary.

5. Show the decimal number 147 in Octal.

6. Show the decimal number 147 in Hexadecimal.

7. Convert this hexadecimal number 5D3₁₆ to Binary.

8. Convert this hexadecimal number 5D3₁₆ to Octal.

9. Convert this hexadecimal number 5D3₁₆ to Decimal.

10. Convert this octal number 1234₈ to Decimal.

11. Convert this octal number 1234₈ to Binary.

12. Convert this octal number 1234₈ to Hexadecimal.

13. Show the decimal number 5.25 in Binary.

14. Convert the binary number 1.101₂ to decimal.

15. Addition: Show 42 + 3 in binary--explaining each time you add and carry (Show your work for credit). Hint: Make a table with powers of 2 as column headings and make the first row equal to the binary value for decimal 42; make the next row binary 3, then add column by column for the total in last row.