## Note on Binary Number System

• 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

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:

1×22+1×21+1×20

=4+2+1

=7

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%

112201
100202
100405
120203

333555
243525
342555
343555

10001102
10110012
11001102
0010112

55
50
65
60

110
105
107
115

130
135
145
150

225
235
230
245

1101001002
1000111012
1110001112
1111111112

11100010102
11010001112
10101010102
11010010002

10000101112
10110011012
11110010102
10101011012

111001012
101010102
110110102
111111112

111000012
101010102
100101012
110010102

1100101012
1011100102
1111111112
1010001112

1750
1755
1700
1753

370
390
375
365
• ## You scored /15

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