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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

Computer Science

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. 16

1. 8

1. 11

d) 2013

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

1. 1

1. 2

1. 4

1. 10

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

1. 15

b) 255

c) 65,535

d) 10,000,000

1. The largest single digit in octal is

1. 1

1. 7

1. 8

1. 10

1. The largest single digit in hexadecimal is

1. 1

1. 8

1. F

1. 9

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

a) 113

b) 179

c) 133

d) 10,110,011

1. Eight raised to the power zero is

1. 0

1. 1

1. 8

1. -8

1. Eight raised to the power one is

1. 0

1. 1

1. 8

1. -8

1. 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. range

1. parameter

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

1. heaviest bit

1. least significant digit

1. most significant digit

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

1. 9

1. 10

1. 24

1. 12

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

1. 9

1. 17

1. 26

d) 110

1. How many bits are there in one byte?

1. 1

1. 4

1. 8

1. 10

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

1. bit

1. blip

1. signal

1. character

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

1. a bit op

1. a left shift

1. a right shift

1. a complex equation

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

1. a bit op

1. a left shift

1. a right shift

1. a complex equation

1. The base 8 number system is called

1. octal

1. fractal

1. ochodecimal

1. The base 2 number system is called

1. binary

1. fractal

1. bitly

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

b) 102 < 18

c) 1012 < 108

d) 1012 < 58

1. 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

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

b) 108 < 116

c) 118 < 1016

d) 128 < A16

1. 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

1. 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

1. The decimal number 9 is equivalent to the hexadecimal

1. A

1. 9

1. 10

d) 1001

1. The base 16 number system is called

1. octal

1. fractal

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

1. one

1. two

1. three

1. eight

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

1. two

1. four

1. eight

1. sixteen

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

a) 1/10

b) -10

c) -1/10

d) None of these

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

b) 2.25

c) 4.25

d) 10.01

1. The octal number 1.28 is equivalent in decimal to

a) 1.25

b) 8.16

c) 8.25

d) 12

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

b) 10.5

c) 11.25

d) None of these

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

b) 0.18

c) 0.116

d) None of these

1. The digit furthest to the right is usually the

1. lightest bit

1. least significant digit

1. most significant digit

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

1. range

1. field

1. base

1. parameter

1. 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

1. fractal point

1. division point

Analytic questions

1. Convert this binary number 1010110102 to Decimal.

1. Convert this binary number 1010110102 to Octal.

1. Convert this binary number 1010110102 to Hexadecimal.

1. Show the decimal number 147 in Binary.

1. Show the decimal number 147 in Octal.

1. Show the decimal number 147 in Hexadecimal.

1. Convert this hexadecimal number 5D316 to Binary.

1. Convert this hexadecimal number 5D316 to Octal.

1. Convert this hexadecimal number 5D316 to Decimal.

1. Convert this octal number 12348 to Decimal.

1. Convert this octal number 12348 to Binary.

1. Convert this octal number 12348 to Hexadecimal.

1. Show the decimal number 5.25 in Binary.

1. Convert the binary number 1.1012 to decimal.

1. 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.

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