Data representation - Number systems (paper 1)

Question 1

what is the order of binary representation

Answer 1

Bit, Nibble, Byte, Kibibyte, Mebibyte, Gigabyte, Tebibyte, Pebibyte, Exibyte

Ben Nibbled Bens Keish Made Gratefully To Paul

Question 2

how and why do computers use binary to represent all forms of data

Answer 2

• computers are made up of switches : 2 states= off (0) and on (1)
• all data needed to be converted into binary to be processed by computer
• data is processed using logic gates and stored in registers

Question 3

how many bits are in a Nibble

Answer 3

4

Question 4

how many bits are in a Byte

Answer 4

8

Question 5

how many bytes are in Kibibyte

Answer 5

1024 bytes

Question 6

how many KiB are in a MiB

Answer 6

1024 KiB

Question 7

how to convert binary into positive denary

Answer 7

• write out the place holders above the binary - 1,2,4,8,16….
• add the numbers which have a 1 under

Question 8

what base system does denary have

Answer 8

base of 10

Question 9

how to convert positive denary into binary

Answer 9

• start with the most significant bit
• then keep going down

Question 10

what number system does hexadecimal have

Answer 10

base 16

Question 11

what are 10 - 15 represented by in hexadecimal

Answer 11

A-F

Question 12

how to convert binary into hex

Answer 12

• split 8-bit binary number into 2 nibbles of 4 bits
• convert each nibble separately - starting from 1,2,4,8

Question 13

convert 01001111 into hex

Answer 13

0100 = 4
1111 = 15 = F
4F

Question 14

how convert hex into binary

Answer 14

• convert each hex value into a 4-bit binary value
• join to make a byte

Question 15

convert 7E into binary

Answer 15

7 = 0111
E = 14 = 1110
01111110

Question 16

how to convert hex into denary

Answer 16

• multiply hex digits by their column place values 16 and 1
• add results**

Question 17

convert 5B into denary

Answer 17

5 x 16 = 80
B = 11
11 x 1 = 11
80 + 11 = 91

Question 18

how to convert denary into hex

Answer 18

• work out how many 16 go into the number = 1st hex digit
• take remainder = 2nd hex digit

Question 19

convert 219 into hex

Answer 19

219 / 16 = 13 r 11
13 = D
11 = B
DB

Question 20

how and why hexadecimal is used as a beneficial method of data representation.

Answer 20

• hex is easier to humas to read + remember than binary - shorter representation than binary

Question 21

2 main uses

what are the 4 uses of hex within areas of computer science

Answer 21

• Colour values in photo editing + web design –> 1Hex no. = 1 nibble
• MAC addresses = unique number given to all Internet-connected devices - each address written in hex
• IPv6 addresses
• Unicode

Question 22

what are the rules of binary addition

Answer 22

0+0 = 1
0+1 = 1
1+1 = 0 carry 1
1+1+1 = 1 carry 1

Question 23

add 01011011 + 00111010

Answer 23

01011011
00111010
——————-
10010101

Question 24

when will an overflow occur

Answer 24

• occurs when the result of adding 2 binary numbers is greater than the bits allowed:
  
  • max value in a 8-bit register = 255
• a computer or a device has a predefined limit
  that it can represent or store, e.g. 16-bit

Question 25

Effect of right logical shifts:

Answer 25

x2 each time

Question 26

what is the effect of shifting to the right

Answer 26

divide by 2 each time

Question 27

what happens binary shifts and what happens in the empty spaces when the binary is shifted

Answer 27

- The positive binary integer is **multiplied or divided** according to the shift performed - The **most significant bit(s) or least significant bit(s) are lost** - Bits shifted from the end of the register are lost and **zeros** are shifted in at the opposite end of the register

Question 28

when does an issue occur regarding the precision in binary shifts

Answer 28

- when **odd numbers** are divided / numbers that can fully divide --> byte **cannot represent fractional numbers** - when 1 is lost at the end = last digit dropped is odd

Question 29

what is the meaning of unsigned and signed representation

Answer 29

**Unsigned** = binary number can only represent **positive numbers** **Signed** = represent both **positive + negative** numbers

Question 30

in twos complement what does the left most bit represent

Answer 30

it is the **sign bit**: - **1** = **negative** - **0** = **positive**

Question 31

what is the maximum and minimum value a signed 8-bit register can hold

Answer 31

max = 127 min = -128

Question 32

what number is the leftmost bit in binary two's complement if the number is negative

Answer 32

1

Question 33

how to convert negative denary number into binary

Answer 33

- work out **positive binary equivalent** - **flip** all bits - **add 1**

Question 34

convert -21 into binary

Answer 34

21 = 0001 0101 flip = 1110 1010 +1 = ____________1 convert:**1110 1011**

Question 35

how do you convert negative twos complement binary number to denary

Answer 35

- flip - add 1 - work it **positive denary** - switch it to the **negative equivalent**