Transcript Binary Numbers

Binary Numbers
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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
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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.
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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
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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