## Note on Binary Arithmetic and Conversion

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#### Conversion from Decimal to Binary

To convert the decimal number to binary number, repeated division by two is needed.

Examples: Convert following into binary numbers:

1. (45)10= (101101)2
 2 45 1 2 22 0 2 11 1 2 5 1 2 2 0 1

=(101101)2

2. (225)10= (10111001)2
 2 225 1 2 112 0 2 56 0 2 23 1 2 11 1 2 5 1 2 2 0 1

= (10111001)2

#### Conversion from Binary to Decimal

To convert binary to the decimal number system, multiply given number by 2.

1. (1101)2=(?)10

=1x23+ 1 x 22+ 0x 21+ 1x 20
=8 + 4 + 0 + 1
=13

 A B A+B 0 0 0 0 1 1 1 0 1 1 1 0 with carry 1
Examples:
1. 1100 + 1111= 11011
 1 Carry 1 1 0 0 1 1 1 1 11 0 1 1

#### Rules for Binary Multiplication

 A B A*B 0 0 0 0 1 0 1 0 0 1 1 1
Example:

• To convert decimal number to binary number, repeated division by two is needed.
• To convert binary to decimal number system, multiply given number by 2.
.

### Very Short Questions

Binary numbers are added to the same manner as decimal numbers. There are only four possible combinations resulting from the addition of two binary digits.

 A B A+B 0 0 0 0 1 1 1 0 1 1 1 10

i.e. 0 carry 1

The rules for subtraction are the same in the binary system as in the decimal system. The result of the subtraction of binary digit is either 0 or 1.

Rules for binary subtraction:

 A B A-B 0 0 0 1 0 1 1 1 0 0 1 1
i.e. due to borrowing from the next column

Binary numbers are multiplied in the same manner as decimal numbers. We need to remember the rules of binary addition.

Rules for binary multiplication:

 A B A×B 0 0 0 1 0 0 0 1 0 1 1 1

=1x23+ 1 x 22+ 1x 21+ 0x 20
=8 + 4 + 2 + 0
=14

 2 45 1 2 22 0 2 11 1 2 5 1 2 2 0 1

=(101101)2

0%
• ### According to binary addition, 1 + 1 equals to :

11

1

2

0 with carry 1

• ### According to binary number system, 11 equals to :

None of the answers are correct
00001011
01011011
11011011

2221
11001
2211
3210

16

2

8

10

• ### To convert decimal number to binary number,repeated division by _____ is needed.

2

1

10

None of the answers are correct

• ## You scored /5

Forum Time Replies Report

##### SAKSHYAM

Rules for substracting binary digits??

Conver0100

##### Bibek

Rules of binary subtraction