Special Lecture Exercise for Lec02 (CS1102 - Section C01/CB1/CC1)
www.cs.cityu.edu.hk/~helena
Casual Discussion, Warm-up Questions, and Lecture Demo Exercises
1. Complete the following table to show the conversion between four number systems:
Decimal [Base 10]
Digits: 0-9
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Binary [Base 2]
Octal [Base 8]
Digits: 0,1
Digits: 0-7
0
1
10
11
100
101
110
111
1000
1001
1010
1011
1100
1101
1110
0
1
2
3
4
5
6
7
10
11
12
13
14
15
Hexadecimal [Base 16]
Digits: 0-9,A,B,C,D,E,F
0
1
2
3
4
5
6
7
8
9
A
B
C
2. (i) Complete the table on the right which shows the powers of 2:
(ii). Fill in the blanks:
(a) 0 1 0 0 0 0 1 1 (2) = __________________(10)
(b) 1 1 1 1 0 0 1 1 (2) = __________________(16)
(c) 1 1 0 1 0 0 1 1 (2) = __________________(8)
20
21
22
23
24
25
26
27
28
29
210
=1
=2
=4
=8
=
=
=
=
=
=
=
3. Why are followings most commonly used?
Number System
Reason to use
(Base 2) Binary
- 2 digits:
0,1
(Base 8) Octal
- 8 digits:
0-7
(Base 10) Decimal
- 10 digits: 0-9
(Base 16) Hexadecimal - 16 digits: 0-9,A-F
1
Special Lecture Exercise for Lec02 (CS1102 - Section C01/CB1/CC1)
4. Choose "Least significant" or "Most significant"
to describe each underlined digit:
Note: significant means "important"
www.cs.cityu.edu.hk/~helena
I have $375.15
Most / least significant digit
Most / least significant digit
5. Consider using 2's complements to represent a range of -ve to + ve numbers
 If we use 4 bits to represent a range of numbers in 2's complement, they can be -8(10) to 7(10)
 If we use 8 bits to represent a range of numbers in 2's complement, they can be -128(10) to ____(10)
 In 2's complement, The left-most bit is always __.
6. Summary / More practices on Binary Arithmetic
What you learnt
More Examples, Practices
[Slide 9] Conversion from Decimal to Binary
(Whole numbers) Repeated division
(a) 26(10) = _____________(2)
[Slide 22] Binary Addition (note: carry digits)
[Slide 22] Binary Subtraction (note: borrow digits)
[Slide 23] Binary Multiplication
[Slide 23] Binary Division
[Slide 27-32] To deal with -ve numbers
Using Two's Complement
(b) 0011(2) +0101(2) = ____________(2)
(c) 1001(2) -0011(2) = ____________(2)
(d) 101(2) x 110(2) = ____________(2)
(e) 111000(2) / 110(2) = _____________(2)
(f) 5 - 2 = _____________(2)
2