Assignment Due March 12,2005
Basic Concepts
When we first learned about numbers, we were taught that, in the
decimal system, things are organized into columns:
"H" is the hundreds column, "T" is the tens
column, and "O" is the ones column. So the number "193" is
1hundreds plus 9tens plus 3ones.
(1 x 100) + (9 x 10) + (3 x 1)
The ones column = 100. The tens column = 101. The hundreds column
= 102.
So: 193 can be seen as:
The number 193 is really {(1x102)+(9x101)+(3x100)} => (1 x
100) + (9 x 10) + (3 x 1).
The decimal system uses the digits 09 to represent numbers.
The binary system works under the exact same principles as the
decimal system, only it operates in base 2 rather than base 10.
In other words, instead of columns being
They are:
Instead of using the digits 09, we only use the digits 0 and
1.
The binary system uses the digits 0 and 1 to represent numbers.
The first column we fill is the rightmost column, which is 20,
or 1. For each additional power of 2 we need to use an extra
column to the left.
The number 5 in binary is 101:
This is: 1x22) + (0x21) + (1x20) = (1 x 4) + (0 x 2) + (1 x 1).
= 4 + 0 + 1
Converting From Binary to Decimal
Example:
What is the decimal value of the binary number 11001101?
Solution:
1 
Power of 2 
27 
26 
25 
24 
23 
22 
21 
20 
2 
Decimal 
128 
64 
42 
16 
8 
4 
2 
1 
3 
Binary 
1 
1 
0 
0 
1 
1 
0 
1 
4 
Multiply 
128 
64 
0 
0 
8 
4 
0 
1 
Sum the product in row # 4
 128 + 64 + 0 + 0 + 8 + 4 + 0 + 1
 205
This conversion can also be done without the chart:
1111010
 (1x 26) +(1x 25) +(1x 24) +(0x 23) +(1x 22)
+(1x 21)
 64 + 32 + 16 + 8 + 0 + 2 + 0
= 122
Exercises:
Convert the following binary numbers to decimal:
1.10
2.111
3.10101
4.11110
5.11001
6.101011
7.1100010
8.1111000
9.11111010
10.11101110
