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Binary Number System

Types of Number System

  • Based on how many n digits a number system uses, Base/Radix of the number system is n.

Number System

Binary

Octal

Decimal

Decimal

  • Base = 10

  • Base = 16

  • Base = 2

  • Base = 8

  • eg. 1011101

  • eg. 12345670

  • eg. 1234567890

  • eg. 

1234567890ABCDEF

  • A most used system of numbers in the world.

  • Often used in computing as a compacter.

  • Used in digital devices.

  • Occasionally used in computing.

What is Binary?

  • A binary or base 2 number systems having 2 symbols 0 and 1s.

  • Each binary digit represents a power of 2.

  • Here is the binary number representation.

(Position)

  • This digit is often called bits.

  • This branch of mathematics known as Boolean algebra. 

  • Concerned logic and truth value.

8

7

6

1

1

5

4

3

2

1

Nibble

Byte

Word

Double word

1 Bit

  • 4 - bit binary

  • 8 - bit binary

  • 16 - bit binary

  • 32 - bit binary

1

1

1

0

0

0

Conversion

Binary to decimal converion :

  • To convert from binary to decimal, multiply each digit in the binary number by successive powers of 2, and then add the results together.

  • Let the binary no. 11011001 is to be converted to decimal.

8

7

6

5

4

3

2

(Position)

1

1

1 X 2   = 1 X     1 =     1

0

0 X 2   = 0 X     2 =     0

1

0 X 2   = 0 X     4 =     0

2

1 X 2   = 1 X     8 =     8

3

1 X 2   = 1 X   16 =   16

4

0 X 2   = 0 X   32 =     0

5

1 X 2   = 1 X 128 = 128

1 X 2   = 1 X   64 =   64

7

6

1 + 8 + 16 + 64 + 128    =  217

11011001 binay = 217 decimal

0

0

1

0

0

1

0

0

1

Binary to decimal converion :

  • Write down the decimal number and to continually divide-by-2 (two) to give a result and a remainder of either a “1” or a “0” until the final result equals zero.

  • For example, take 27 as decimal no. and see below.

Successive division by 2

Remainders

1

 

1

​

0

​

1

​

1

LSB

MSB

Read the remainders from the botter to up.

27 decimal = 11011 binary

  • Here are the 4-bit binary nos. with a decimal value.

Application

  • In digital electronic circuitry using logic gates, the binary system is used internally by almost all modern computers and computer-based devices. 

  • Because of its straightforward implementation.

5 volt = TRUE ( 1 )

0 volt = False ( 0 )

The computer understands only 0 or 1 (digital signal).

  • All computer language and programming is based on the 2-digit number system used in digital encoding.

  • Used in most electric counters.

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