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TM112: Block 1 > part 1, binary data representation and computation > Flashcards

part 1, binary data representation and computation Flashcards

1
Q

explain what a logic circuit is

A

this is a combination of logic gates that can perform more complex operations and outputs than could be accomplished with a single logic gate

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2
Q

how many representations of 0 does twos compliment have

A

this has only one representation of 0

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3
Q

with this a 0 represents a positive (+) and a 1 represents a negative (-)

A

in sign magnitude the first bit represents the sign of the number, but what does the 0 bit represent and what does the 1 bit represent

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4
Q

upper case letters start with 0100

A

what 4 bits do uppercase letters start with in ASCII

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5
Q

what are the 3 distinct parts of scientific notation

A
  1. a sign
  2. a mantissa (the decimal part beginning with digits 0-9 )
  3. an exponent (the power of 10)
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6
Q

this is a standard used to represent numbers and letters that are currently in use across the globe it became the standard in 2007

A

what is UTF-8 and when did it become the standard to be used

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7
Q

what does de morgans law ultimately mean

A

** ****** *** ultimately means that it is possible to build any logic circuits using a combination of just two logic gates

  1. And gate and NOT gate
  2. OR gate and NOT gate
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8
Q

this has only one representation of 0

A

how many representations of 0 does twos compliment have

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9
Q

this uses 8 bytes to store a floating point number

A

how many bytes does a double (double precision) use to store a float

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10
Q

the algorithm says that if both signs are the same for the numbers you are adding then add the smaller number to the larger number

A

your following the sign magnitude algorithm for addition. the numbers you are adding have the same sign. by the algorithm what is the step you should follow

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11
Q
A

describe how the truth table for the NOT operation would look with an input of A

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12
Q
  1. a sign
  2. a mantissa (the decimal part beginning with digits 0-9 )
  3. an exponent (the power of 10)
A

what are the 3 distinct parts of scientific notation

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13
Q

this works by outputing a 1 if two or more inputs are both 1

A

explain how the AND operation works

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14
Q

the original 7-bit ASCII has been preserved by this standard

A

what has been preserved by UTF-8

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15
Q

this uses a variable amount of bytes up to 6

A

how many bytes does UTF-8 use

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16
Q

what is a truth table

A

a truth table will take all possible inputs and then output all the posssibilitys of the operation you are performing on the inputs

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17
Q

how far apart are lower case letters and upper case letters in ASCII

A

they differ by 32 this is because the 32nd bit is flipped on or off depending on using lower or upper case letter

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18
Q

this is any integer greater than or equal to 0

A

what is an unsigned integer

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19
Q

let max = 4

if max is 4 then 3 + 2 would cause an overflow
the following pseudo code would warn us of this overflow before we perform the calculation

if (3 >= Max - 2) {
log overflow}

A

explain the technique of using a programming languages max value constant to help avoid an overflow when using addition

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20
Q

what is sign magnitude

A

this is a type of encoding that allows for signed integers

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21
Q

he was a friend of george boole and is the founder of the de morgans law

A

who is augustus de morgan and what is he the founder of

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22
Q

if we have n bits. what is the expression for the amount of unsigned integers that can be represented

A

the amount of unsigned integers that can be represented is 2^n

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23
Q

what has been preserved by UTF-8

A

the original 7-bit ASCII has been preserved by this standard

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24
Q

how many bytes does a typical float have

A

this has 4 bytes

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25
Q
  1. it can cause overflow
  2. it is able to be used for subtraction, division and multiplication, by turning each of these calculations into an addition problem
A

what are two important notes about the twos complement addition algorithm

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26
Q

Subtract 00110000 from the ASCII code

A

A character representing a digit, n, is stored as an 8-bit ASCII code. It needs to be converted into an 8 bit sign-magnitude representation for the positive numerical value, n. What is the algorithm for doing this?

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27
Q
  1. a sign
  2. a mantissa (the decimal part. always begins with 1)
  3. an exponent (a power of 2)
A

what are the 3 rules for scientific notation for binary numbers

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28
Q

using n bits in twos compliment. what is the expression for the largest positive integer that can be represented

A

the largest positive integer that can be represented is

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29
Q

this is a number that has a decimal point or A number without a fixed number of digits before and after the decimal point

A

what is a floating point number

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30
Q

this works by dedicating the first bit to the sign of the number when the first bit flips and negative numbers are being represented the largest negative number is the first number to be represented

A

how does twos complement work

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31
Q

using n bits in twos complement what is the expression for how many positive signed integers can be represented including 0

A

the amount of positive signed integers that can be represented including zero is

2^n / 2

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32
Q

using sign magnitude. if we have n bits what is the expression for the largest magnitude that can be represented

A

the expression for the largest magnitude that can be represented using n bits is

2^n/2 - 1

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33
Q

the expression for the amount of signed integers that can be represented is

2^n

A

using twos complement what is the expression for how many signed integers can be represented

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34
Q

when we have n bits the expression for the range of unsigned integers that can be represented including 0 is

2^n - 1

A

if we have n bits. what is the expression for the range of unsigned integers that can be represented when including 0

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35
Q

developed in 1963 this was a common way to represent letters and numbers in binary

A

what is ASCII and when was it developed

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36
Q

excluding zero the amount of negative signed integers that can be represented excluding 0 is

2^n/2

A

using n bits in twos complement what is the expression for how many negative signed integers can be represented excluding zero

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37
Q

the negative number with the largest magnitude that can be represented will be

2^n / 2

A

using n bits in twos complement what is the expression for the negative number with the largest magnitude that can be represented

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38
Q

what is ASCII and when was it developed

A

developed in 1963 this was a common way to represent letters and numbers in binary

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39
Q

how is a float represented in a computer

A

it is represented in binary scientific notation

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40
Q

** ****** *** ultimately means that it is possible to build any logic circuits using a combination of just two logic gates

  1. And gate and NOT gate
  2. OR gate and NOT gate
A

what does de morgans law ultimately mean

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41
Q

descibe the 1-bit full adder circuit

A
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42
Q

your following the sign magnitude algorithm for addition. the calculation you are performing involves a negative number and a positive number you have performed the calculation but now need to decide on the sign for the sum.

how is this achieved

A

by the algorithm after you have performed the calculation of a positive number and a negative number the sign of the sum can be found by looking back at the original calculation numbers and while still ignoring the signs decide which is greater the sign of that number will be the sign of the sum

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43
Q

the largest positive integer that can be represented is

2^n / 2 - 1

A

using n bits in twos compliment. what is the expression for the largest positive integer that can be represented

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44
Q

using twos complement what is the expression for how many signed integers can be represented

A

the expression for the amount of signed integers that can be represented is

2^n

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45
Q

how many inputs does the half adder have

A

the **** ***** has two inputs being the two bits you wish to add together

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46
Q
  1. any OR gate can be replaced by a combination of AND and NOT gates
  2. any AND gate can be replaced by a combination of OR and NOT gates
A

what two things does de morgans law tell us

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47
Q

an overflow will occur and the next number will display as a -8 that is 1000 in twos compliment

A

using twos compliment we have the binary number 0111. there are only four bits available. if 1 is added to this number what will happen

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48
Q

this has 3 inputs

  1. binary number a
  2. binary number b
  3. carry from the previous addition
A

how many inputs does the 1-bit full adder have

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49
Q

describe how the OR truth table would look

A
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50
Q

descibe how the OR logic gate is drawn

A
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51
Q

explain the technique of use arithmetic interchangeably to help mitigate overflow or underflow

A

one technique taken is to perform arithmetic interchangeable. that is, instead of performing many additions and multiplication or subtraction and division these should be used interchangeably with the intermediate value where possible.

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52
Q

what 4 bits do numbers start with in ASCII

A

numbers start with 0011

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53
Q
A

describe how the AND logic gate is drawn

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54
Q

this is able to add together binary numbers greater than 1 bit

A

what is the 1-bit full adder able to acomplish

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55
Q
A
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56
Q

what two things does de morgans law tell us

A
  1. any OR gate can be replaced by a combination of AND and NOT gates
  2. any AND gate can be replaced by a combination of OR and NOT gates
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57
Q

what 4 bits do lower case letters start with in ASCII

A

lower case letters start with 0110

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58
Q

describe how the NOT logic gate (inverter) is drawn

A
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59
Q

what are the two steps of the twos complement addition algorithm

A
  1. add the binary numbers
  2. discard the leftmost bit if the answer exceeds the number of available bits
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60
Q

who is augustus de morgan and what is he the founder of

A

he was a friend of george boole and is the founder of the de morgans law

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61
Q

how many outputs does the 1-bit full adder have

A

this has two outputs

  1. the sum
  2. the carry
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62
Q

using n bits in twos complement what is the expression for how many negative signed integers can be represented excluding zero

A

excluding zero the amount of negative signed integers that can be represented excluding 0 is

2^n/2

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63
Q

using n bits in twos complement what is the expression for the negative number with the largest magnitude that can be represented

A

the negative number with the largest magnitude that can be represented will be

2^n / 2

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64
Q

how does sign magnitude work

A

this works by dedicating the first bit to the sign of the number. all bits there after are the magnitude of the number.

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65
Q

this is made up of two half adders

A

describe what the 1-bit full adders logic circuit is made up off

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66
Q

this occurs when the number in the mantissa is to small to represent in binary. this happens because there are not enough bits available for the exponent

A

when does an underflow occur

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67
Q

what does ASCII stand for

A

American standard code for information interchange

68
Q

positive values start with a 0. the same as sign magnitude

A

what bit do positive values start with in twos compliment

69
Q

when does an underflow occur

A

this occurs when the number in the mantissa is to small to represent in binary. this happens because there are not enough bits available for the exponent

70
Q

the **** ***** is able to add together 2 single bits

A

what is the half adder able to perform

71
Q

in sign magnitude the first bit represents the sign of the number, but what does the 0 bit represent and what does the 1 bit represent

A

with this a 0 represents a positive (+) and a 1 represents a negative (-)

72
Q

this occurs when the integer required exceeds the number of bits available

A

when does overflow occur

73
Q

A character representing a digit, n, is stored as an 8-bit ASCII code. It needs to be converted into an 8 bit sign-magnitude representation for the negative numerical value, -n. What is the algorithm for doing this?

A

Subtract 00110000 from the ASCII code and add 1000 0000

74
Q

the 1 in the mantissa before the decimal point is not stored by the computer. this is because it is always a 1 and so is usually hardwired into the processors floating point unit

A

when a computer stores a float or a double which part is never stored

75
Q

describe how the AND logic gate is drawn

A
76
Q

the expression for the largest magnitude that can be represented using n bits is

2^n/2 - 1

A

using sign magnitude. if we have n bits what is the expression for the largest magnitude that can be represented

77
Q
  1. add the binary numbers
  2. discard the leftmost bit if the answer exceeds the number of available bits
A

what are the two steps of the twos complement addition algorithm

78
Q

2^3=8

so the answer is 8 unsigned integers can be represented by 3 bits

A

if we have 3 bits how many unsigned integers can be represented

79
Q

unicode transformation format-8

A

what does UTF-8 stand for

80
Q

your following the sign magnitude algorithm for addition. the numbers you are adding have the same sign. by the algorithm what is the step you should follow

A

the algorithm says that if both signs are the same for the numbers you are adding then add the smaller number to the larger number

81
Q

how does twos complement work

A

this works by dedicating the first bit to the sign of the number when the first bit flips and negative numbers are being represented the largest negative number is the first number to be represented

82
Q

describe what logic operations are and name there inventor

A

these perform operations on on a given iput or inputs. the inventor of these was george boole

83
Q

explain how the AND operation works

A

this works by outputing a 1 if two or more inputs are both 1

84
Q

by the algorithm to add a negative number and a positive number you must ignore the signs and subtract the smaller number from the larger number

A

your following the sign magnitude algorithm for addition. the calculation you are performing involves a negative number and a positive number by the algorithm what is the next step to add these numbers

85
Q

if we have n bits. what is the expression for the range of unsigned integers that can be represented when including 0

A

when we have n bits the expression for the range of unsigned integers that can be represented including 0 is

2^n - 1

86
Q

this is a popular type of encoding that allows for signed integers

A

what is twos complement

87
Q

how many inputs does the 1-bit full adder have

A

this has 3 inputs

  1. binary number a
  2. binary number b
  3. carry from the previous addition
88
Q

what is a floating point number

A

this is a number that has a decimal point or A number without a fixed number of digits before and after the decimal point

89
Q

the computer would say the equality is false even though it is true. this is because of the precision problem computers suffer from

A

if you asked a computer for the equality of
0.1 + 0.1 + 0.1 = 0.3. what would its answer be and why

90
Q
A

describe the half adder circuit

91
Q

these perform operations on on a given iput or inputs. the inventor of these was george boole

A

describe what logic operations are and name there inventor

92
Q

describe how the OR operation works

A

this works by outputting 1 (true) if either or both the inputs is a 1 (true)

93
Q
A

descibe how the OR logic gate is drawn

94
Q

how many bytes does UTF-8 use

A

this uses a variable amount of bytes up to 6

95
Q
  1. the first bit is assigned to the sign. 0 for positive 1 for negative
  2. the next 8 bits are the exponent
  3. the mantissa is the last 23 bits
A

a computer typically stores a float using 4 bytes but how does it use this memory

96
Q

what is twos complement

A

this is a popular type of encoding that allows for signed integers

97
Q

describe what the 1-bit full adders logic circuit is made up off

A

this is made up of two half adders

98
Q

this works by outputting 1 (true) if either or both the inputs is a 1 (true)

A

describe how the OR operation works

99
Q

by the algorithm if both signs are negative for the numbers you are adding then there sum will also be negative.

this same rule applies for positive numbers.
if both signs are positive for the numbers you are adding then there sum will also be positive.

A

your following the sign magnitude algorithm for addition. you have two calculations one is adding two negative numbers together the other is adding two positive numbers together. by the algorithm for each calculation how would you handle the sign for the sum of each calculation

100
Q

the amount of unsigned integers that can be represented is 2^n

A

if we have n bits. what is the expression for the amount of unsigned integers that can be represented

101
Q

if we have 3 bits how many unsigned integers can be represented

A

2^3=8

so the answer is 8 unsigned integers can be represented by 3 bits

102
Q
A

describe how the truth table for the AND operation would look

103
Q

what are the 3 rules for scientific notation for binary numbers

A
  1. a sign
  2. a mantissa (the decimal part. always begins with 1)
  3. an exponent (a power of 2)
104
Q

what are two important notes about the twos complement addition algorithm

A
  1. it can cause overflow
  2. it is able to be used for subtraction, division and multiplication, by turning each of these calculations into an addition problem
105
Q

it is represented in binary scientific notation

A

how is a float represented in a computer

106
Q
A

describe how the NOT logic gate (inverter) is drawn

107
Q
A

describe how the OR truth table would look

108
Q

this has 4 bytes

A

how many bytes does a typical float have

109
Q

American standard code for information interchange

A

what does ASCII stand for

110
Q

describe the half adder circuit

A
111
Q

a computer typically stores a double using 8 bytes but how does it use this memory

A
  1. the first bit is assigned to the sign. 0 for positive 1 for negative
  2. the next 11 bits are the exponent
  3. the mantissa is the last 52 bits
112
Q

the amount of positive signed integers that can be represented including zero is

2^n / 2

A

using n bits in twos complement what is the expression for how many positive signed integers can be represented including 0

113
Q

how many outputs does the half adder have

A

the **** ***** has two outputs

  1. the sum
  2. the carry
114
Q
A

describe the half adder symbol

115
Q

how many bytes does a double (double precision) use to store a float

A

this uses 8 bytes to store a floating point number

116
Q
  1. the NOT operation
  2. the AND operation
  3. the OR operation
A

name 3 common logic operations

117
Q

lower case letters start with 0110

A

what 4 bits do lower case letters start with in ASCII

118
Q

what bit do positive values start with in twos compliment

A

positive values start with a 0. the same as sign magnitude

119
Q

using twos compliment we have the binary number 0111. there are only four bits available. if 1 is added to this number what will happen

A

an overflow will occur and the next number will display as a -8 that is 1000 in twos compliment

120
Q
  1. use arithmetic interchangeable (+, -, +) instead of (+, +, +) or (/, x, /) instead of (/, /, /)
  2. make use of the programming languages max and min constant values
A

what are two techniques taken that can help mitigate overflow or underflow

121
Q

describe how the truth table for the AND operation would look

A
122
Q

your following the sign magnitude algorithm for addition. you have two calculations one is adding two negative numbers together the other is adding two positive numbers together. by the algorithm for each calculation how would you handle the sign for the sum of each calculation

A

by the algorithm if both signs are negative for the numbers you are adding then there sum will also be negative.

this same rule applies for positive numbers.
if both signs are positive for the numbers you are adding then there sum will also be positive.

123
Q

your following the sign magnitude algorithm for addition. the calculation you are performing involves a negative number and a positive number by the algorithm what is the next step to add these numbers

A

by the algorithm to add a negative number and a positive number you must ignore the signs and subtract the smaller number from the larger number

124
Q

describe how the truth table for the NOT operation would look with an input of A

A
125
Q

if you asked a computer for the equality of
0.1 + 0.1 + 0.1 = 0.3. what would its answer be and why

A

the computer would say the equality is false even though it is true. this is because of the precision problem computers suffer from

126
Q

it handles this by giving the closest value it can, given the number of bits it has

A

how do computers handle a sum such as 1/3 which is an infinite repeating decimal

127
Q

using n bits what will the binary representation be for the negative number with the largest magnitude

A

using n bits the binary representation for the negative number with the largest magnitude will be

1 followed by all n 0s

128
Q

explain the technique of using a programming languages max value constant to help avoid an overflow when using addition

A

let max = 4

if max is 4 then 3 + 2 would cause an overflow
the following pseudo code would warn us of this overflow before we perform the calculation

if (3 >= Max - 2) {
log overflow}

129
Q

how does the NOT operation work

A

this works by flipping the bit

130
Q

a computer typically stores a float using 4 bytes but how does it use this memory

A
  1. the first bit is assigned to the sign. 0 for positive 1 for negative
  2. the next 8 bits are the exponent
  3. the mantissa is the last 23 bits
131
Q

name 3 common logic operations

A
  1. the NOT operation
  2. the AND operation
  3. the OR operation
132
Q

this is a type of encoding that allows for signed integers

A

what is sign magnitude

133
Q

how is the number 0 represented in sign magnitude

A

this represents 0 twice. firstly as +0 then again as -0

134
Q

this is a combination of logic gates that can perform more complex operations and outputs than could be accomplished with a single logic gate

A

explain what a logic circuit is

135
Q

Subtract 00110000 from the ASCII code and add 1000 0000

A

A character representing a digit, n, is stored as an 8-bit ASCII code. It needs to be converted into an 8 bit sign-magnitude representation for the negative numerical value, -n. What is the algorithm for doing this?

136
Q

numbers start with 0011

A

what 4 bits do numbers start with in ASCII

137
Q

A character representing a digit, n, is stored as an 8-bit ASCII code. It needs to be converted into an 8 bit sign-magnitude representation for the positive numerical value, n. What is the algorithm for doing this?

A

Subtract 00110000 from the ASCII code

138
Q

a truth table will take all possible inputs and then output all the posssibilitys of the operation you are performing on the inputs

A

what is a truth table

139
Q

descibe the 1-bit full adder symbol

A
140
Q

what 4 bits do uppercase letters start with in ASCII

A

upper case letters start with 0100

141
Q

describe the half adder symbol

A
142
Q

what is the 1-bit full adder able to acomplish

A

this is able to add together binary numbers greater than 1 bit

143
Q
A
144
Q

what are two techniques taken that can help mitigate overflow or underflow

A
  1. use arithmetic interchangeable (+, -, +) instead of (+, +, +) or (/, x, /) instead of (/, /, /)
  2. make use of the programming languages max and min constant values
145
Q

when a computer stores a float or a double which part is never stored

A

the 1 in the mantissa before the decimal point is not stored by the computer. this is because it is always a 1 and so is usually hardwired into the processors floating point unit

146
Q

what is UTF-8 and when did it become the standard to be used

A

this is a standard used to represent numbers and letters that are currently in use across the globe it became the standard in 2007

147
Q

what bit do negative values start with in twos complement

A

negative values start with a 1. the same as sign magnitude

148
Q

the **** ***** has two inputs being the two bits you wish to add together

A

how many inputs does the half adder have

149
Q

when does overflow occur

A

this occurs when the integer required exceeds the number of bits available

150
Q

how do computers handle a sum such as 1/3 which is an infinite repeating decimal

A

it handles this by giving the closest value it can, given the number of bits it has

151
Q

one technique taken is to perform arithmetic interchangeable. that is, instead of performing many additions and multiplication or subtraction and division these should be used interchangeably with the intermediate value where possible.

A

explain the technique of use arithmetic interchangeably to help mitigate overflow or underflow

152
Q

what does UTF-8 stand for

A

unicode transformation format-8

153
Q

this works by dedicating the first bit to the sign of the number. all bits there after are the magnitude of the number.

A

how does sign magnitude work

154
Q
A

descibe the 1-bit full adder symbol

155
Q

this works by flipping the bit

A

how does the NOT operation work

156
Q
  1. the first bit is assigned to the sign. 0 for positive 1 for negative
  2. the next 11 bits are the exponent
  3. the mantissa is the last 52 bits
A

a computer typically stores a double using 8 bytes but how does it use this memory

157
Q

what is the half adder able to perform

A

the **** ***** is able to add together 2 single bits

158
Q

this represents 0 twice. firstly as +0 then again as -0

A

how is the number 0 represented in sign magnitude

159
Q

this has two outputs

  1. the sum
  2. the carry
A

how many outputs does the 1-bit full adder have

160
Q

negative values start with a 1. the same as sign magnitude

A

what bit do negative values start with in twos complement

161
Q

using n bits the binary representation for the negative number with the largest magnitude will be

1 followed by all n 0s

A

using n bits what will the binary representation be for the negative number with the largest magnitude

162
Q

by the algorithm after you have performed the calculation of a positive number and a negative number the sign of the sum can be found by looking back at the original calculation numbers and while still ignoring the signs decide which is greater the sign of that number will be the sign of the sum

A

your following the sign magnitude algorithm for addition. the calculation you are performing involves a negative number and a positive number you have performed the calculation but now need to decide on the sign for the sum.

how is this achieved

163
Q

the **** ***** has two outputs

  1. the sum
  2. the carry
A

how many outputs does the half adder have

164
Q

they differ by 32 this is because the 32nd bit is flipped on or off depending on using lower or upper case letter

A

how far apart are lower case letters and upper case letters in ASCII

165
Q

what is an unsigned integer

A

this is any integer greater than or equal to 0

166
Q
A

descibe the 1-bit full adder circuit

167
Q

in binary ASCII what do each of these begin with

  1. number
  2. lowercase letters
  3. uppercase letters
A

TM112: Block 1 (4 decks)

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