Download Binary Numbers

Binary Numbers
Press any key to begin.
In order to understand the binary numbering
system lets first look at our decimal system.
• The decimal numbering system consists of the
numbers 0 through 9.
• After nine we place a 1 in the tens column
and start again with 0. Which gives us 10.
• The decimal system is also known as base 10
because it is based on the 10 numbers 0 – 9.
0
1
2
3
4
5
6
7
8
9
1 0
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Binary Numbers have only two digits 0 or 1
Binary is known as Base 2
Decimal
Binary
0
0
1
1
2
10
3
11
4
100
5
101
6
110
7
111
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As you can see it would take a lot of time to create
charts to represent Binary numbers.
An easier way is to use the powers of 2
20 = 1
21 = 2
22 = 4
24 = 16
25 = 32
26 = 64
23 = 8
27 =128
Lets place the above calculations into a chart that will
make it easy to convert a binary number to a decimal
number.
27
26
25
24
23
22
21
20
128 64 32 16
8
4
2
1
Press any key to continue…
Use the chart to convert the binary number to decimal.
27
128
26
64
25
32
24
16
23
8
22
4
21
2
20
1
0
0
1
0
1
0
0
1
1
2
4
x
x
x
1
0
0
=
=
=
8
16
32
x
x
x
1
0
1
= 8
= 0
= 32
64
128
x
x
0
0
=
=
Total
1
0
0
0
0
= 41
Note: The bit to
the far right is the
Least Significant
Bit (LSB) and will
determine if the
number is even or
odd.
Press any key to continue…
Use the chart to convert the binary number to decimal.
27
128
26
64
25
32
24
16
23
8
22
4
21
2
20
1
0
1
1
1
1
1
1
1
=
=
=
1
1
1
1
=
=
=
=
1
1
2
4
8
16
32
64
1
8
16
32
64
1
x
x
x
x
x
x
x
128
x
0
=
0
1
2
4
Total
= 127
Note: if consecutive
bits from the right
are all 1’s
Then the answer is
the next power of 2
minus 1
In this case
128 – 1 = 127
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Take a piece of paper and convert the binary number to decimal.
Press any key when you have the answer.
27
128
26
64
25
32
24
16
23
8
22
4
21
2
20
1
1
0
1
1
1
0
1
0
1
2
4
x
x
x
0
1
0
=
=
=
8
16
32
64
128
x
x
x
x
x
1
1
1
0
1
= 8
= 16
= 32
= 0
= 128
Total
0
2
0
= 186
Press any key to continue…
The largest number that can be represented using
an 8 bit binary number is 255.
28
27
256 128
1
26
64
25
32
24
16
23
8
22
4
21
2
20
1
1
1
1
1
1
1
1
Remember the rule – if all the digits are 1 then
the number is the next power of 2 minus 1
256 – 1 = 255
Converting a binary number to a decimal
number is a simple task if you understand the
chart below and how to use it.
27
128
26
64
25
32
24
16
23
8
The End
22
4
21
2
20
1