Data Representation

Question 1

What are electronic computers (except ENIAC) based on?

Answer 1

Based on two state devices:

transistors and logic gates.

Question 2

What are 2 state devices

Answer 2

Devices that can only be in one of two conditions at any time e.g. on/off, yes/no, 1/0

Question 3

In two-state representation, what do we need to distinguish between electronically?

Answer 3

Electronically, we need to distinguish only between, for example:

Voltage and no voltage
Current and no current
Switch on and off
Electrical pulse and no electrical pulse

Question 4

What are numeration systems?

Answer 4

All numeration systems are representational — i.e. a form of coding.

Question 5

What type of notation does the decimal numeral system have?

Answer 5

The decimal numeral system has a positional notation.

Question 6

How do you convert from decimal to binary

Answer 6

1. Divide the number by two and if it is not divisible by 2 then write a 1 beside it, otherwise a 0.
2. Divide the new number by 2
3. Repeat until you get to 0. (When you get to 1, it counts as a 1 not 0 AND NO NUMBER NEEDED FOR WHEN YOU ARE AT 0)
4. Write the combinations of 1’s and 0’s from bottom to top to get the binary code.

Question 7

How do you convert from binary to decimal

Answer 7

1. Write out the binary code from left to right.
2. Start from the right hand side and do 2^0, 2^1, 2^n.
3. Multiply the numbers from the previous steps by the binary number 1/0 assigned to it and then add up all the numbers.

Question 8

what does subscript 10 and subscript 2 mean

Answer 8

10 - represents the decimal system
2 - represents the binary system

Question 9

What are the rules when doing binary addition

Answer 9

0 + 0 = 0
1 + 0 = 1
1 + 1 = 0 and carry the 1 onto the next column
1 + 1 + 1 = Write 1 and carry 1

When you have 1 + 1 and have a carried on 1, you write 1 and carry the other 1.

Question 10

What are the rules when doing binary subtraction

Answer 10

0 - 0 = 0
1 - 0 = 1
1 -1 = 0
0 - 1 = 1 because you borrow 1 from the next column so the zero essentially becomes a 2.

Question 11

How can the two states of a collection of two-state devices be used?

Answer 11

The two states of a collection of two-state devices can be used to encode a number in binary representation.

Question 12

What do computer systems do with two-state devices?

Answer 12

Computer systems use the two states of two-state devices to encode numbers in binary representation — this is exactly what happens in computer systems!

Question 13

How many bit pattern can a cell of n bits hold

Answer 13

2^n bit pattern

Each bit has 2 possibilities so we do 2x2x2 n number of times which is the same as 2^n

Question 14

How many different numbers can we store in a byte

Answer 14

256 different numbers, from 0 to 255

Question 15

What is Binary-Coded Decimal (BCD)?

Answer 15

Binary-Coded Decimal (BCD) is a system where decimal digits are coded directly as 4 bits.

Question 16

What is Binary-Coded Sexagesimal and how many bits does it use?

Answer 16

Binary-Coded Sexagesimal uses 6 bits to represent values in sexagesimal (base 60), like in time.

Question 17

What are Gray Codes (reflected binary code)?

Answer 17

Gray Codes, or reflected binary codes, are codes in which successive values differ in only a single digit.

Question 18

What are the three main representations of signed integers?

Answer 18

The three main representations of signed integers are:

Sign and Magnitude
One’s Complement
Two’s Complement

Question 19

How do we represent integers from -(2^n - 1) to (2^n -1) in a cell of n+1 bites in sign and magnitude

Answer 19

The first bit represents the sign of the integer - 0 is positive and 1 is negative

The remaining n bits represent the magnitude (using normal binary)

Question 20

What are the advantages of sign and magnitude

Answer 20

Easy to read
Symmetric about 0

Question 21

What are the disadvantages of using sign and magnitude

Answer 21

There are 2 representations of 0
Only 255 values are represented in a cell
Arithmetic becomes unnecessarily complicated - there are cases for each combination of signs.

Question 22

How do we represent integers using 1’s complement

Answer 22

Positive integers are represented by adding a leading 0.

Negative integers are represented by swapping 1’s and 0’s in n. The leading bit still represents the sign

Question 23

Advantages and disadvantage of 1’s complement

Answer 23

Simplifies arithmetic, but it leaves us with 2 representations of 0.

Question 24

How does 2’s complement represent integers

Answer 24

Like 1’s complement, we represent -n by swapping 0’s and 1’s in n, and then binary adding 1

E.g. Step 1: Write 6 in binary
6 = 00110

Step 2: Invert all bits (change 0 to 1 and 1 to 0)
00110 → 11001

Step 3: Add 1 using normal binary addition
11001 + 1 = 11010

Final answer:
−6 = 11010

Question 25

How to turn -37 into 2's complement

Answer 25

1. +37 = 00100101 2. 00100101 -> 11011010 3. 11011011

Question 26

How many representations of zero are there in two’s complement?

Answer 26

1

Question 27

In two’s complement, what does a 1/0 in the most significant bit position indicate?

Answer 27

A 1 in the leftmost (“most significant”) bit indicates the number is negative and a 0 means positive

Question 28

Is the number line symmetrical about 0 in two’s complement representation?

Answer 28

No. The number line is not symmetrical because there is one more representation of negative numbers than positive numbers.

Question 29

What is the advantage of arithmetic in 2’s complement representation?

Answer 29

Arithmetic on signed numbers can be carried out in one step — we don’t need to worry about sign and magnitude separately.

Question 30

In 2’s complement, why is addition and subtraction straightforward?

Answer 30

Once we can handle signed numbers, we can do subtraction as well as addition using the same binary operations.

Question 31

Give an example of adding +7 and -3 in 2’s complement (in binary).

Answer 31

00000111 = +7 11111101 = -3 00000100 = +4 REMEMBER ONLY NEED TO DO +1 AND SWITCH 1'S AND 0'S WHEN MAKING A POSITIVE NUMBER NEGATIVE.

Question 32

How do we store character data?

Answer 32

We give a unique bit pattern to each character.

Question 33

How many bit patterns are used for upper and lower case letters?

Answer 33

26 patterns for upper case letters, and 26 patterns for lower case letters.

Question 34

Why can individual characters usually be stored within a single byte?

Answer 34

Because fewer than 128 bit patterns are usually sufficient.

Question 35

How are strings stored?

Answer 35

Strings of characters can be stored in a succession of bytes.

Question 36

What does ASCII stand for and how many bits does it use?

Answer 36

ASCII = American Standard Code for Information Interchange, and it uses 7-bit representation.

Question 37

What does UNICODE provide compared to ASCII?

Answer 37

UNICODE (32-bit) can represent over 2 billion characters, including alphabets in different languages, emojis, symbols, etc.

Question 38

Why was UTF-8 created?

Answer 38

To have backward compatibility with ASCII and avoid wasted space.

Question 39

What kind of character encoding is UTF-8?

Answer 39

UTF-8 is a variable-width character encoding.

Question 40

Why do we use octal or hexadecimal notation for binary numbers?

Answer 40

Writing or displaying binary directly is tedious, so we use octal (base 8) or hexadecimal (base 16) for convenience.

Question 41

Which digits does octal notation use?

Answer 41

0, 1, 2, 3, 4, 5, 6, 7.

Question 42

Which digits does hexadecimal notation use?

Answer 42

Hexadecimal uses 0–9 and A, B, C, D, E, F.

Question 43

How many bits does one octal digit correspond to?

Answer 43

One octal digit corresponds to three bits.

Question 44

How many bits does one hexadecimal digit correspond to, and what is it also called?

Answer 44

One hexadecimal digit corresponds to four bits, also known as a nibble.

Question 45

How to go from decimal to BCD

Answer 45

Split the number into each number (where possible) e.g. 58 into 5 and 8. Make each number using only 8,4,2,1. E.g. 5 = 4 + 1 and 8 = 8 so 5 = 0101 and 8 = 1000 Put a 1 when the number is present and a 0 where not