1. Nat 4/5 Computing Science Lesson 1: Binary
Computer Systems
Nat 4/5 Computing Science
Lesson 1:
Binary

2. Lesson Aims By the end of this lesson: You will be able to:
Describe what an integer is
Represent positive integers in binary using up to 8 Bits
State three advantages of the binary number system
Represent negative numbers using binary (Nat 5)
Represent real numbers using binary (Nat 5)

3. The Decimal & Binary Systems
Nat 4/5
The Decimal & Binary Systems
We use the decimal(denary) or base 10 system
This means we have 10 digits : 0-9
Computers use the binary or base 2 system
There are only two digits: 0 and 1
Each figure is known as a bit
Binary digit
Because of our ten fingers?
Off and On

4. Nat 4/5
Decimal Numbers
Lets look at how a decimal number is made up: 173
Technically this is:
Hundreds
Tens
Units 1 7 3
102
101
100
Hundreds
Tens
Units 1 7 3

5. Nat 4/5
Binary Numbers
Because Binary is only made up of two digits (0 and 1) instead of 10 (as in Decimal), the column headings will be different.
This is represented as: 24 23 22 21 20 16 8 4 2 1

6. Nat 4/5
Binary Numbers
Lets look at how 173 is stored in binary:
128 64 32 16 8 4 2 1
The binary number is calculated by adding together the value of the columns with a 1. =
= 173

7. How to convert from Binary
Nat 4/5
How to convert from Binary
Create your table with the values in the top
Insert your binary value into the table
Add the place values that have a binary 1 in them: = 102
128 64 32 16 8 4 2 1 1

8. Advantages of the Binary system
Nat 4/5
Advantages of the Binary system
There are less rules of arithmetic, this makes it easier to program.
0’s and 1’s are easier to represent digitally in computer systems.
Any drop in voltage does not affect the data.

9. Summary Binary only has two values– 0 & 1
Nat 4/5
Summary
Binary only has two values– 0 & 1
A single 0 or 1 is known as a bit
Binary Digit
The place values in binary start on the right at 1 and double every time going to the left.
Advantages of Binary:
There are less rules of arithmetic.
0’s and 1’s are easier to represent.
Any drop in voltage doesn’t effect data.

10. What about negative numbers?
Nat 5
What about negative numbers?
Integers include:-
-123, -89, 0, 45, , etc
Positive and negative integers are represented using two’s complement

11. Two’s complement Write -7 :- +7 using 8 bits 0000 0111
Nat 5
Two’s complement
Write -7 :-
+7 using 8 bits
Change 1’s and 0’s
Add
So -7 is

12. Nat 5
Twos complement tasks
Questions 1 and 2 on Worksheet 1a

13. Real numbers Decimal Fractions:- 1/10 1/100 1/1000 …. As a fraction
Nat 5
Real numbers
Decimal Fractions:-
1/10 1/100 1/1000 …. As a fraction
…. As a decimal
Binary Fractions:-
½ ¼ /8
…. as a fraction
…. as a decimal

14. Real numbers task
Question 3 on Worksheet 1a

15. Floating point representation
From Maths we know that:-
= x 102
Mantissa x Base Exponent
In binary :-
= = x 2 101
5 in decimal is 101 in binary

16. Floating point representation
Nat 5
Floating point representation
The computer stores the mantissa & exponent of a real number
x 2 101
Mantissa =
Exponent = 101

17. Nat 5
Floating point task
Question 4 Worksheet 1a