Note on Binary Number System

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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.
.

Very Short Questions

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

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

    246210

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

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

    1100102

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

    11010112

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

    100001112

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

    111111112

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

    420

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

    840

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

    535

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

    255

     

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

    225

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

    405

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

    110110110012

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

    370
    390
    375
    365
  • You scored /15


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