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Binary Number System

Notes, Exercises, Videos, Tests and Things to Remember on Binary Number System

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  • Note
  • Things to remember
  • Exercise
  • Quiz

It is necessary to review the decimal number system at first to understand more about binary number system. Decimal number system refers to base 10 positional notation. It uses ten different symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) arranged using positional notation. Positional notation is used when a number larger then 9 needs to be represented; each position of a digit signifies how many groups of 10, 100, 1000, etc. are contained in that number. For example,

4251

4 \(\times\) 1000 + 2 \(\times\) 100 + 5 \(\times\) 10 + 1

4\(\times\) 103+ 2\(\times\) 102 + 5\(\times\) 101 + 4\(\times\) 102

Binary number system
Binary number system

0 and 1 are used in binary number system which is arranged using positional notation (the digit 0 and 1 as a symbol). When a number larger than 1 needs to be represented, the positional notation is used to represent, the positional notation is used to represent how many groups of 2, 4, 8 are contained in the number. For example,

Let's consider the number 30

30 ÷ 2 = 15 Remainder 0

15 ÷ 2 = 7 Remainder 1

7 ÷ 2 = 3 Remainder 1

3 ÷ 2 = 1 Remainder 1

1 ÷ 2 = 0 Remainder 1



  • A number is a mathematical object used to count, measure and label.
  • The binary number system always uses only two different symbols ( the digit 0 and 1) that are arranged using positional notation. 
  • We can subtract a binary number from the another binary number.
.

Questions and Answers

Click on the questions below to reveal the answers

Solution:

110102

=1×24+1×23+0×22+1×21+0×20

=16+8+0+2+0

=26

Solution:

110102

=1×24+1×23+0×22+1×21+0×20

=16+8+0+2+0

=26

Solution:

1010112

=1×25+0×24+1×23+0×22+1×21+1×20

=32+0+8+0+2+1

=43

Solution:

10102= 1×23+0×22+1×21+0×20

=8+0+2+0

=10

Solution:

11102 = 1×23+1×22+1×21+0×2o

=8+4+2+0

= 14

Solution:

1×24+0×23+1×22+0×21+1×2o

=16+0+4+0+1

=21

Solution:

=1×25+0×24+1×23+0×22+1×21+0×20

=32+0+8+0+2+0

=42

Solution:

1×25+1×24+0×23+0×22+1×21+1×20

= 32+16+0+0+2+1

=51

Solution:

2125

= 2×52+1×51+2×50

= 2×25+1×5+2×1

= 50+5+2

= 5710

Solution:

3145

=3×52+1×51+4×50

= 3×25+1×5+5+4

= 75+5+4

= 8410

Solution:

245

= 2×51+4×5°

= 2×5+4×1

=10+4

=1410

Solution:

3545

= 3×52+2×51+4×5°

= 75+10+4

= 8910

Solution:

2 105 1
2 52 0
2 26 0
2 13 1
2 6 0
2 3 1
2 1 1
0

∴ 10510 = 11010012

Solution:

111111112

= 1×27+ 1×26 + 1×25+ 1×24 + 1×23 + 1×22 +1×21 + 1×20

= 128 + 64 + 32 + 16 + 8 + 4 +2 + 1

= 225

0%
  • Convert the following numbers into quinary numbers:

    64510

    100405
    100202
    120203
    112201
  • Convert the following numbers into quinary numbers:

    246210

    333555
    343555
    342555
    243525
  • Convert the following decimal number into binary number.
    7510

    10110012
    11001102
    10001102
    0010112
  • Convert the following binary number into decimal numbers.

    1100102

    65
    50
    55
    60
  • Convert the following Binary Number into Decimal Number.

    11010112

    115
    110
    105
    107
  • Convert the following  binary number into decimal number.

    100001112

    150
    145
    130
    135
  • Convert the binary number into decimal number.

    111111112

    225
    245
    230
    235
  • Convert the following decimal number into binary number.

    420

    1110001112
    1111111112
    1101001002
    1000111012
  • Convert the following decimal number into binary number.

    840

    11010010002
    11010001112
    10101010102
    11100010102
  • Convert the following decimal number into binary number.

    535

    11110010102
    10110011012
    10000101112
    10101011012
  • Convert the following decimal number into binary number.

    255

     

    111001012
    111111112
    101010102
    110110102
  • Convert the following decimal number into binary number.

    225

    100101012
    111000012
    101010102
    110010102
  • Convert the following decimal number into binary number.

    405

    1010001112
    1011100102
    1111111112
    1100101012
  • Convert the following binary number into decimal numbers.

    110110110012

    1755
    1753
    1700
    1750
  • Convert the following  binary number into 1011101112

    375
    365
    390
    370
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