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

Rules for Binary Addition

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.

Rules for binary addition:

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 :

    2


    11


    0 with carry 1


    1


  • According to binary number system, 11 equals to :

    None of the answers are correct
    11011011
    00001011
    01011011
  • 1100 + 1111 equals to ________

    2211
    3210
    11001
    2221
  • To convert binary to decimal number system, multiply given number by ______.

    8


    10


    2


    16


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

    2


    1


    10


    None of the answers are correct


  • You scored /5


    Take test again

DISCUSSIONS ABOUT THIS NOTE

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SAKSHYAM

Rules for substracting binary digits??


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Bijay

Conver0100


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Bibek

Rules of binary subtraction


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