Binary

DO NOW

BINARY

LEARNING OBJECTIVES

1. Understand the binary code basic.

2. Perform simple binary operations, using positive

numbers.

3. Be able to convert to and from Binary to Denary.

HOW DO COMPUTERS COMMUNICATE?

Computers communicate using a two digit eletronic signal system

called binary (0 and 1).

These shape system correspond to the electrical

on/off signals. It makes it useful for the computer to

processing and storing data.

WHAT IS BINARY & DENARY ?

Binary: is the base 2 number system, which uses only two
digits (0 and 1).
The binary digits (0 and 1) are called bits.

To understand solve Binary, we must first understand Denary.

Denary:
is the base-10 number system that uses digits 0 to 9 for

counting and arithmetic.

Denary = 0 1 2 3 4 5 6 7 8 9

BINARY (BASE 2) IN A
COMPUTER

Binary Exist in the digits 0 and 1, and

they are called bits.

• Inside a computer, if there is an electrical voltage

on a wire. It means that wire is transmitting a

1 (one), which also means it's ON.

• If there's no voltage, the wire is transmitting 0

(Zero), which means it's OFF.

• It allows computers to store and manipulate data

using a system of switches that can be turned on

or off.

Questions Ahead.

Multiple Choice

What is Binary?

• A system that uses 10 digits

• A system that uses 2 digits

• A system that uses 8 digits

• A system that uses 16 digits

Multiple Choice

What is Denary?

• A system that uses 2 digits

• A system that uses 8 digits

• A system that uses 16 digits

• A system that uses 10 digits

Multiple Choice

What are the Binary Digits 0 and 1 called?

• Units

• Bytes

• Bits

• Nibbles

Multiple Choice

How do Computers Communicate?

• Using letters and symbols

• By sending electrical signals

• By using their own language

• By sending light signals

Multiple Choice

If there is an electrical voltage on a wire, what is the wire transmitting?

• 0

• A bit

• A nibble

• 1

Fill in the Blank

If there is no voltage, the wire is transmitting ____, which means it’s ____

,

POSITIONAL NUMBER SYSTEM

A positional number system is a way of writing numbers where the value of
each digit depends on its position.

• Think of the Positional Number System as Place Value.

For example, in our usual math's number system, the number 123 means:

Each digit’s value changes based on where it is in the number.

So, 1 = 100

2 = 20

3 = 3

Therefore, the combined number = 123.

Hundreds

Tens

Ones

1

2

3

BINARY POSITIONAL NUMBER
SYSTEM (PLACE VALUE)

Binary uses a Positional System (Place Value) of 8 Bits.

The binary place value increases by 2 digits. This is why it is also
called a based 2 systems.

128

64

32

16

8

4

2

1

Questions Ahead.

Multiple Choice

What is the Positional Number System?

• A system where the value of a digit depends on its position

• A system where all digits have the same value

• A system with only two digits

• A system where numbers are randomly arranged

Multiple Choice

Another word for Positional System is?

• Non-Positional System

• Decimal System

• Place-Value System

• Alphabetic System

Multiple Choice

What is the Binary Positional Value?

• 10, 100, 1000

• 1, 10, 100

• 1, 2, 4, 8, 16, 32, 128

• 1, 3, 5, 7, 9, 12

Multiple Choice

Binary allows computers to?

• Understand only letters

• Solve human language instantly

• Store words in sentences

• Store and manipulate data using a system of switches (ON/OFF)

BINARY CONVERSION

CONVERTING BINARY TO DENARY

EXAMPLE OF CONVERTING
BINARY TO DENARY

Example 1:
Convert the 8 Bit Binary (0 0 1 1 0 1 0 1) into Base 10
(Denary).

Remember: 1 = ON & 0 = OFF.
To convert this binary, we only calculate the 1s:
(1 x 32) + (1 x 16) + (1 x 4) + (1 x1 ) = 53

128

64

32

16

8

4

2

1

0

0

1

1

0

1

0

1

EXAMPLE OF CONVERTING
BINARY TO DENARY

Example 2:
Convert the 8 Bit Binary (0 1 0 1 1 0 1 0) into Base 10
(Denary).

Remember: 1 = ON & 0 = OFF.
To convert this binary, we only calculate the 1s:
(1 x 64) + (1 x 16) + (1 x 8) + (1 x 2 ) = 90

128

64

32

16

8

4

2

1

0

1

0

1

1

0

1

0

EXAMPLE OF CONVERTING
BINARY TO DENARY

Example 3: We Do
Convert the 8 Bit Binary (1 1 1 1 1 1 1 1) into Base 10
(Denary).

Remember: 1 = ON & 0 = OFF.
To convert this binary, we only calculate the 1s:

128

64

32

16

8

4

2

1

ACTIVITY 1:

Complete
Activity 1
on Class

Note.

“Convertin

g 8 Bits
Binary to
Denary”.

BINARY CONVERSION

CONVERTING DENARY TO BINARY

EXAMPLE OF CONVERTING
DENARY TO BINARY

Example 1:
Convert the 49 Into 8 bit Binary.

Remember: 1 = ON & 0 = OFF.
To convert this binary, we only calculate the 1s:
32 + 16 + 1 = 49.

128

64

32

16

8

4

2

1

1

1

1

ACTIVITY 2:

Complete
Activity 2
on ClassNote.

“Converting

Denary to Binary”.