Name: Review 1 Complete?

[ ]

Corrected? [ ]

Mark: Review 2 Complete? [ ]

/202 Corrected? [ ]

1.1 Number Systems

1. Data Representation

iGCSE Computer Science

1.1.1 Number Systems Page 1 of 35

Syllabus
1.1.1 Number Systems Page 2 of 35

1.1 Number System Key Terms

Example term in English You write the definition in English here

here:

Write the term in your You write the definition in your language here
language here: 在此用您的语言写出定义
Вы пишете определение на своем языке здесь
ここにあなたの言語で定義を書く
여기에 해당 언어로 정의를 작성합니다.

Denary (decimal) number

system

Binary number system

Hexadecimal (hex) number

system

Integer

Registers
1.1.1 Number Systems Page 3 of 35

Logic gates

Error codes

Media Access Control (MAC)

address

Internet Protocol (IP)

address

HyperText Mark-up
Language (HTML)

Overflow error

Logical shift
1.1.1 Number Systems Page 4 of 35

Two’s complement

Most significant bit (MSB)

Least significant bit (LSB)

1.1.1 Number Systems Page 5 of 35

Binary
1. Binary is a number system made up of ___’s and ___’s. It has a base of _____ this means that
each number to the left is ________ as big as the one on the right. Digital computers only
process information in_____________. All data and program instructions are stored as binary.
Pictures and movie are / are not stored as binary. Binary data is processed using ___________
and stored in _____________.
[8 marks]

2. Complete the table below

29 28 27 24 22 20

1024 64 32 8 2

[11 marks]

3. Convert these positive binary integers into denary/decimal

8 4 2 1

_______ 0 0 0 0

_______ 0 1 1 0

_______ 0 1 0 1

_______ 1 0 1 0

_______ 1 1 1 1

[5 marks]
1.1.1 Number Systems Page 6 of 35

4. Convert these positive binary integers into denary/decimal

_______ 0 0 0 0 0 1 1 1

_______ 0 0 0 1 0 1 0 1

_______ 1 0 0 1 1 1 1 1

_______ 0 1 1 0 0 0 0 0

_______ 0 1 1 1 0 1 1 1

_______ 1 1 1 0 1 0 0 0

_______ 1 0 0 1 0 0 0 1

_______ 1 1 0 1 1 1 1 1

[8 marks]

5. What is the largest number you can represent with the sizes below?

1 bit = __________
2 bits = __________
4 bits = __________
8 bits = __________
[4 marks]

6. How many different values can be represented with the sies below?

1 bit = __________
2 bits = __________
4 bits = __________
8 bits = __________
[4 marks]

7. What is the formula to calculate; (using n to represent the number of bits)

a) The largest representable: ____________________

b) The number of values that can be represented: ___________________
[2 marks]
1.1.1 Number Systems Page 7 of 35

8. Show with working how you convert 10110011 into denary

[2 marks]
1.1.1 Number Systems Page 8 of 35

9. Convert the below 16-bit binary numbers. Show your working.

a)

32,768 16,384 8,192 4,096 2,048 1,024 512 256 128 64 32 16 8 4 2 1

1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0

___________

b)

32,768 16,384 8,192 4,096 2,048 1,024 512 256 128 64 32 16 8 4 2 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

___________

c)

0 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1

___________
d)

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

__________
[8 marks]
1.1.1 Number Systems Page 9 of 35

10. Convert the below decimal numbers into binary using the minus method (show your working)
a) 36

___________
b) 65

___________
c) 98

___________
d) 26

___________
e) 45

___________
f) 12

___________
[12 marks]
1.1.1 Number Systems Page 10 of 35

11. Convert the below decimal numbers into binary using the remainder method (show your
working)
a) 74

___________
b) 39

___________
c) 28

___________
d) 91

___________
e) 173

___________
f) 17

___________

[12 marks]
1.1.1 Number Systems Page 11 of 35

12. Show how to convert 205 into binary using your chosen method (show your working).

Chosen method: __________________

___________
[2 marks]

13. Show how to convert 134 into binary using your chosen method (show your working).
Chosen method: __________________

___________

[2 marks]

14. Show how to convert 231 into binary using your chosen method (show your working).
Chosen method: __________________

___________
[2 marks]
1.1.1 Number Systems Page 12 of 35

15. The white keys on a digital piano are represented using binary.
In the example below keys B, E and F are pressed. Note that B, E and F are represented by 1.

Binary 0 1 0 0 1 1 0

The key combination B, E and F is given the denary code 38

a) F and G are pressed

i. What is the binary code for F and G being pressed?

Answer________________[1]
ii. What is the denary code for F and G being pressed?

Answer________________[1]
b) What is the denary code of A, D and G being pressed?

Answer________________[1]
c) What combination of keys are pressed with the Denary code: 25

Answer________________[1]
d) How many possible key combinations are there

Answer________________[1]
1.1.1 Number Systems Page 13 of 35

Hexadecimal
16. Hex has a base of ________.
[1 mark]

17. Hex uses the numbers _____ - 9 and the letters _____ - _____.
[2 marks]

18. Convert denary 89 into hex using the steps shown.

i. Convert 89 into binary

ii. Split the byte into 2 nibbles

iii. Convert the individual nibbles into their hex value 0-F

____________ ____________
[1 marks]

19. Convert the denary below values into hex (via binary). Show working.
a) 94

____________ ____________
[1 mark]
1.1.1 Number Systems Page 14 of 35

b) 5

c)

____________ ____________
[1 mark]

c) 34

d)

____________ ____________
[1 mark]
d) 100

_________
[1 mark]
e) 201

_________
[1 mark]
1.1.1 Number Systems Page 15 of 35

f) 46

_________
[1 mark]
g) 255

_________
[1 mark]

20. Convert the following denary values into hex (3 hex digits)

a) 262

_________
[1 mark]
b) 300

_________
[1 mark]
c) 186

_________
[1 mark]
1.1.1 Number Systems Page 16 of 35

d) 257

_________
[1 mark]
e) 310

_________
[1 mark]
1.1.1 Number Systems Page 17 of 35

21. Convert these binary numbers into hex. Show working.

a) 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

________________
[4 marks]

b) 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1

________________
[4 marks]

c) 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0

________________
[4 marks]

d) 1 0 1 0 1 1 1 0 0 1 0 0 1 1

________________
[4 marks]
1.1.1 Number Systems Page 18 of 35

22. Convert the below hex numbers to denary (direct method) show your working.
a) 9B

_________
[1 mark]
b) AF

_________
[1 mark]
c) 24

_________
[1 mark]
d) E3

_________
1.1.1 Number Systems Page 19 of 35

[1 mark]
e) AC3

_________
[1 mark]
f) 6F7

_________
[1 mark]
23. Convert the below hex numbers to denary (via binary) show your working
a) 8D

_________
[1 mark]
b) 3E

_________
1.1.1 Number Systems Page 20 of 35

[1 mark]
c) 7A

_________
[1 mark]
d) A4F

_________
[1 mark]
e) 1CD

_________
[1 mark]
f) 2AE

_________
[1 mark]
1.1.1 Number Systems Page 21 of 35

24. Show how to convert 2C5(hex) into denary using your chosen method (show your working)
Chosen method: __________________

___________
[2 marks]
1.1.1 Number Systems Page 22 of 35

Current Uses of Hexadecimal

25. What are some of the current uses of hex?

i. _______________________________________
ii. _______________________________________
iii. _______________________________________
[3 marks]

26. Give 2 reasons hex would be used?

i. ________________________________________
ii. ________________________________________
[2 marks]

27. What is a memory dump?

______________________________________________________________________________
______________________________________________________________________________
[1 mark]
28. What does a MAC address do?

______________________________________________________________________________
[1 mark]

29. What does RGB stand for?

__________________________________________________
[1 mark]

30. What is the colour code for Chocolate Brown?

_________________________
[1 mark]
1.1.1 Number Systems Page 23 of 35

Binary Addition
31. Perform the following binary additions.

a)

1 0 0 1
+ 0 1 0 1
=
[1 mark]
b)

0 0 1 1
+ 1 0 0 1
=
[1 mark]
c)

0 0 1 1
+ 0 0 1 1
=
[1 mark]

d)

0 1 1 1
+ 0 0 0 1
=
[1 mark]
e)

1 1 1 1
+ 0 0 0 1
=
[1 mark]
1.1.1 Number Systems Page 24 of 35

32. Perform the following 8-bit binary additions.

a)

0 1 0 0 1 1 1 1

+ 0 0 0 1 0 0 0 1

=
[1 mark]

b)

1 0 1 1 1 0 1 0

+ 0 0 0 1 0 0 1 0

=
[1 mark]

c)

0 0 1 1 1 0 0 0

+ 0 0 1 1 1 0 0 0

=
[1 mark]

d)

0 0 1 0 1 0 1 1

+ 0 1 1 1 0 0 1 1

=
[1 mark]
e)

1 1 1 1 1 1 1 1

+ 0 0 0 0 0 0 0 1

=
[1 mark]
1.1.1 Number Systems Page 25 of 35

33. What do we call the type of error encountered in Q31(e) and Q32(e)?

________________________________________________
[1 mark]
34. How does this type of error occur?
______________________________________________________________________________
______________________________________________________________________________
[1 mark]
35. What happens to the digit that does not fit into our binary value?

________________________________________________
[1 mark]

Binary Shifts
36. Perform the following binary shifts.
a) Left Shift 1

0 1 0 1 0 1 0 1

[1 mark]

b) Left Shift 2

0 0 0 0 0 1 1 1

[1 mark]
c) Left Shift 3

0 0 0 1 0 0 0 1

[1 mark]
d) Right Shift 1

0 1 1 0 1 0 0 0

[1 mark]
e) Right Shift 2

0 0 0 0 0 0 0 1
1.1.1 Number Systems Page 26 of 35

[1 mark]

37. What happens to bits that are shifted out of the number?

________________________________________________
[1 mark]

38. With a Left Shift, which bit do we lose?

________________________________________________
[1 mark]

39. With a Right Shift, which bit do we lose?

________________________________________________
[1 mark]

40. A Left Shift of 1 has what effect on a binary number?

________________________________________________
[1 mark]

41. A Right shift of 1 has what effect on a binary number?

________________________________________________
[1 mark]

Two’s Complement Binary

42. What type of binary numbers can Two’s Complement represent?

________________________________________________
[2 marks]
43. What does the most significant bit represent?

________________________________________________
[1 mark]
44. If the most significant bit is 1, what does that mean?

________________________________________________
[1 mark]
45. If the most significant bit is 0, what does that mean?

________________________________________________
[1 mark]
1.1.1 Number Systems Page 27 of 35

46. Convert the following Two’s Complement numbers to Denary.

-8 4 2 1

_______ 0 0 0 0

_______ 0 1 1 0

_______ 0 1 0 1

_______ 1 0 1 0

_______ 1 1 1 1

[5 marks]

47. Convert the following Two’s Complement numbers to Denary.

_______ 0 0 0 1 0 1 0 1

_______ 1 0 0 1 1 1 1 1

_______ 0 1 1 0 0 0 0 0

_______ 0 1 1 1 0 1 1 1

_______ 1 1 1 0 1 0 0 0

_______ 1 0 0 1 0 0 0 1

_______ 1 1 0 1 1 1 1 1

[7 marks]
48. Convert the following Denary numbers into Two’s Complement.

-8 4 2 1

-8

-3

-1

[5 marks]
1.1.1 Number Systems Page 28 of 35

49. Convert the following Denary numbers into Two’s Complement.

100

-100

12

-57

-92

17

-17

[7 marks]
1.1.1 Number Systems Page 29 of 35

50. Convert the following Two’s Complement signed binary integers into their positive or negative
equivalent. Show your working.

a. 011011

b. 101110

c. 01010101

d. 110001100

[8 marks]
1.1.1 Number Systems Page 30 of 35

Past Paper Questions

Topic

1. / 12
2. / 5
3. / 3
4. / 4
5. / 2
TOTAL: / 26
1.1.1 Number Systems Page 31 of 35

1.
1.1.1 Number Systems Page 32 of 35

2.

3.
1.1.1 Number Systems Page 33 of 35

4. (a) Positive Denary numbers can also be represented using Twos Complement.
Complete the binary register for the denary value 35.
You must show all your working.
Working space……………………………………………………………………………………………………
…………………………………………………………………………………………………………………………..
…………………………………………………………………………………………………………………………..
…………………………………………………………………………………………………………………………..

Register:

[2]

(b) Twos Complement can also be used to represent Negative Denary Numbers.
Complete the binary register for the denary value -35.
You must show all your working.
Working space……………………………………………………………………………………………………
…………………………………………………………………………………………………………………………..
…………………………………………………………………………………………………………………………..
…………………………………………………………………………………………………………………………..

Register:

[2]
1.1.1 Number Systems Page 34 of 35

5. A shopping centre records the number of customers entering the centre from 2 different entrances.
These values are stored seperately in Binary, before being added together to determine the total
number of customers. The Registers below store the number of customers who have used each
entrance.
Complete the Binary Addition of the 2 registers.
You must show all your working.

Register 1 0 0 1 1 0 0 1 0
Register 2 0 0 1 1 0 0 1 1

Working
Space

Total