1.4.1 Data types - Suprit

Question 1

Define Real Numbers

Answer 1

Positive or negative numbers that typically have a decimal point

Question 2

Define Integer

Answer 2

A whole number

Question 3

Define Characters

Answer 3

Any symbol used by the computer

Question 4

Define String

Answer 4

A collection of characters stored in succession

Question 5

Define Boolean

Answer 5

Represents True or False

Question 6

How do computers store whole numbers?

Answer 6

Computers store whole numbers as binary

Question 7

How many bits make up a nibble?

Answer 7

4 bits

Question 8

How many nibbles make up a byte?

Answer 8

2 nibbles

Question 9

Convert binary number 1101 to denary

Answer 9

13

Question 10

How many bits in a kilobyte?

Answer 10

8000

Question 11

Convert 47 into binary

Answer 11

101111

Question 12

What is 1011 + 1110?

Answer 12

(1)1001
(1) is an overflow

Question 13

What does 0 and 1 at the start of a binary number represent in Sign Magnitude?

Answer 13

0 = Positive Number
1 = Negative Number

Question 14

If 10101101 = 173, what does Sign Magnitude number 010101101 mean in denary?

Answer 14

It’s also 173

Question 15

Convert -105 to a Sign Magnitude number

Answer 15

101101001

Question 16

What is another way to represent positive and negative numbers in binary?

Answer 16

Two’s Complement

Question 17

How do you convert a binary number into Two’s Complement?

Answer 17

Flip all of the individual bits and add 1
Example - 00000111 (7) becomes 11111000 when its initially flipped, and becomes 11111001 (-7) once 1 has been added on.

Question 18

How does subtraction work in Two’s Complement?

Answer 18

It works by adding a negative number to a positive number

Question 19

Subtract 10100 from 01000 in Two’s Complement.

Answer 19

11100 (-4)

Question 20

What base is Hexadecimal?

Answer 20

Base 16

Question 21

What numbers and characters are used in hexadecimal?

Answer 21

Numbers 0-9 and Characters A-F

Question 22

How do you convert Hexadecimal to Binary?

Answer 22

1. Split the Hexadecimal number into individual digits
2. Convert each digit into denary
3. Convert the denary into binary nibbles (4 bits)
4. Combine the nibbles together to get the answer.

Question 23

Convert F1A2 to binary

Answer 23

Answer = 1111000110100010
Explanation -
1. Split F, 1, A, and 2
2. Convert each digit -
F = 15
1 = 1
A = 10
2 = 2
3. Convert the denary into binary nibbles -
15 = 1111
1 = 0001
10 = 1010
2 = 0010
4. Combine them -
1111000110100010

Question 24

How do you convert hexadecimal to denary?

Answer 24

1. Split the Hexadecimal number into individual digits
2. Convert each digit into denary
3. Convert the denary into binary nibbles (4 bits)
4. Combine the nibbles together to get the answer.
5. Convert the binary number into denary

Question 25

Convert F1A2 into denary

Answer 25

Answer = 61858 Explanation - 1. Split F, 1, A, and 2 2. Convert each digit - F = 15 1 = 1 A = 10 2 = 2 3. Convert the denary into binary nibbles - 15 = 1111 1 = 0001 10 = 1010 2 = 0010 4. Combine them - 1111000110100010 5. Convert into binary - 1111000110100010 = 61858

Question 26

What 2 parts make up Floating Point Numbers in Binary?

Answer 26

Mantissa and exponent

Question 27

What does the mantissa represent?

Answer 27

The original number

Question 28

What does the exponent represent?

Answer 28

The shift in the decimal point

Question 29

Is there a leading sign bit in Floating Point Binary?

Answer 29

Yes

Question 30

How do you convert floating point binary into denary?

Answer 30

1. Check if the sign bit is positive (0) or negative (1) 2. The mantissa has the binary point (binary equivalent of decimal point) after the most significant bit. Make sure to place this there. 3. Convert the exponent into decimal (it's in two's complement, so check if it starts with a 0 or a 1) 4. Move the binary point by the same number of times that represents the exponent, moving it left if its negative, and moving it right if its positive. 5. Now convert into denary

Question 31

Convert 01100100111000101 to binary, where this number starts with a sign, has a 10 bit mantissa, and has a 6 bit exponent.

Answer 31

A = 50.4375 Explanation - 1. Check if the sign bit is positive or negative (0 = Positive) 2. Place binary bit after most significant bit in mantissa - 1.100100111 3. Convert the exponent - 000101 = 5 4. Move the binary point depending on the exponent - Exponent = 5, so 1.100100111 = 110010.0111 5. Convert 110010.0111 into denary - 110010.0111 = 50.4375

Question 32

How do you normalise binary numbers?

Answer 32

1. Split the number into its mantissa and exponent 2. Adjust the mantissa so that it starts with 01 or 10 3. Add zeroes to the end depending on how many bits the mantissa was adjusted by 4. Increase/Decrease the exponent depending on how the mantissa was changed.

Question 33

Normalise 000110100101, which has an 8 bit mantissa and a 4 bit exponent

Answer 33

A = 011010000011 Explanation - 1. Split Mantissa and Exponent - M = 00011010 E = 0101 2. Adjust the mantissa so it starts with 01 or 10 - 00011010 = 011010 3. Add zeroes on the end to make it an 8 bit number again - 011010 = 01101000 4. Adjust the exponent - As the mantissa increased by 2 bits, the exponent must decrease by 2 0101 = 0011

Question 34

How do you add floating point binary numbers together?

Answer 34

1. Adjust the exponents so both of them are the same 2. Add the mantissas together 3. Normalise if necessary

Question 35

What is 00001000011 + 00001010010? Both numbers have a sign bit, a 6-bit mantissa and a 4-bit exponent.

Answer 35

1. Adjust exponents so they are both the same - 0011 = 0010 0010 = 0010 000100 becomes 001000 due to the change in exponent 2. Add the mantissas - 001000 + 000101 = 001101 3. Normalise - 00011010010 becomes 00110100001

Question 36

How do you subtract floating point binary numbers?

Answer 36

1. Make the exponents the same 2. Convert the mantissa of the number to be subtracted into two's complement. Do this by flipping all the bits and adding 1 3. Add the numbers 4. Normalise answer

Question 37

What is a logical shift left the same as?

Answer 37

Multiplication

Question 38

What is a logical shift right the same as?

Answer 38

Division

Question 39

What does an AND mask do?

Answer 39

Multiplies inputs, so 1*1 = 1, but anything involving a 0 = 0

Question 40

What does an OR mask do?

Answer 40

If either bit is 1, 1 will be outputted, otherwise 0 will be outputted

Question 41

What happens to the binary number 00101011 when an AND mask of 10111011 has been applied?

Answer 41

A = It becomes 00101011 Explanation - When applying the mask, because the mask is an AND mask, the rules of AND are applied. Therefore, when following the rules, you get 00101011.

Question 42

What happens to the binary number 00101011 when an OR mask of 10111011 has been applied?

Answer 42

A = 10111011 Explanation - The mask is an OR mask, so you apply the rules of OR when applying the mask.