Learning by Doing: CISCO Certified Network ... - SCN Research

Paper Lab: Binary Numbering
Objective:
To learn how to convert binary numbers into decimal numbers and vice versa.
Tools and Materials:
Paper and pencil
“Bit Bashing” worksheet
Background: Converting Binary to Decimal
If I asked you to count from zero to nine I would expect everyone would have no
problem with it. You would respond with “zero-one-two-three-four-five-six-seven-eightnine.”
This is what is known as the decimal (or base 10) system. There are ten possible
combinations available for each column. Each column represents a progressively higher
power of ten. For example the number 532:
10 2 10 1 10 0
100 10 1
532 = 5 3 2
This represents 5 units of 10 2 (10x10=100) which is 5 hundreds, 3 units of 10 1 (10x1=10)
which is 3 tens or 30, and 2 units of 10 0 (1) which is 2. Put them all together and you get
five hundred and thirty-two. Ok. I know you know this stuff already it will just make the
transition to learning stuff on binary easier.
Binary is a base 2 system. Instead of ten numbers we only have two numbers: zero and
one (0 or 1). Like our decimal system our columns each represents a progressively
higher power of 2.
2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0
128 64 32 16 8 4 2 1
Each column heading represents a decimal number with a binary power. To convert
between binary and decimal the rule is simple: Any place you have a “1” you just add the
column heading to get the decimal total. For example, if we were given a binary number
of 01101101 to convert into decimal we would write it under our “bit-bashing” chart.
Then, in any column where a 1 appeared, we would add the column headings together.
That would be our binary to decimal equivalent.
2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0
128 64 32 16 8 4 2 1
0 1 1 0 1 1 0 1
64+32+8+4+1=109
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