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