1. Topic 1: Data Representation
Computer Systems
Topic 1: Data Representation

2. Decimal Number System (3x100) + (4x10) + (5x1) =300 + 40 + 5 =34510
102
101
100
100’s
10’s
1’s 3 4 5
(3x100) + (4x10) + (5x1) =
=34510

3. Conversion of binary to decimal27 26 25 24 23 22 21 20
128’s
64’s
32’s
16’s
8’s
4’s
2’s
1’s 1
(1x128) + (0x64) + (1x32) + (1x16) + (1x8) + (0x4) + (1x2) + (0x1) =
=18610

4. Binary to decimal conversion – practice
1011
Binary to decimal conversion – practice

5. Higher Past Paper Questions
2009 Q1a – Write the binary number as a positive integer.
Higher Past Paper Questions

6. Conversion of decimal to binary – method 1
72 – 64 = 8
8 – 8 = 0

7. Conversion of decimal to binary – method 272
36 R 0
18 R 0
9 R 0
4 R 1
2 R 0
1 R 0
0 R 1 = =
= 72

8. Decimal to binary conversion – practice
134
148
394 29 18 79
273
172
Decimal to binary conversion – practice

9. Higher Past Paper Questions
2005 Q6a – What is the number 385 represented as a binary number?
Higher Past Paper Questions

10. Range of positive integers22 21 20 4 2 1
smallest = 0
largest = 7
So for 3 bits, the range is 0..7

11. Range of positive integers27 26 25 24 23 22 21 20
128 64 32 16 8 4 2 1
smallest = 0
largest = 255
So for 8 bits, the range is
0..28 – 1
So for n bits, the range is 0..2n - 1

12. Range of positive integers - practice
What is the range of positive integers that can be represented using 8 bits?
What is the range of positive integers that can be represented using 12 bits?
What is the range of positive integers that can be represented using n bits?
Range of positive integers - practice

13. Maximum positive integer versus range
Maximum positive integer is the largest number which can be represented by a number of bits e.g. for 8 bits the maximum positive integer is 28 – 1 = 255
The range involves two numbers, the smallest number and the largest number e.g. for 8 bits the range is
Maximum positive integer versus range

14. Higher Past Paper Questions
2011 Q1 – State the largest whole number that can be stored as a 10-bit positive integer.
Higher Past Paper Questions