Transcript Bit Patterns

Math Review
Do you remember, from math class, how
exponentiation operations are
typically represented?
an
a is known as the "base"
n is known as the "exponent".
You might say, "a raised to the power of
n".
Warm Up
Try to find a value for each of the
exponents shown below.
 20 =
 21 =
 22 =
 23 =
 24 + 21 =
Bit Patterns
Computer Number Systems
Scott Baranick & Daniel Velasquez
Bits and Bytes
A
bit is the short name for "binary
digit".
 A bit can store only two values.
Off or On switch
0 or 1
False or True
A
byte is a series of 8 bits or switches.
Bits and Bytes
A
kilobyte is 1024 bytes,
– In other words, 210
–This is often rounded to 1,000
bytes
Bits and Bytes
A
megabyte is either 1000 or
1024 kilobytes.
A gigabyte is either 1000 or
1024 megabytes.
What's next?
Number System Definitions



Binary is just another name for base 2.
Decimal is just another name for base 10.
Hexadecimal is just another name for base 16.
Decimal vs. Binary
101
1 x 102 +
0 x 101 + 1 x 100
= 10110
1 0 12
1 x 22
+
0 x 21
+
1 x 20
= 510
Counting in Base 10
0
+ 1
1
+ 1
2
+ 1
3
.
.
9
+ 1
10
Counting in Base 2
 "Computer
Science Unplugged"
Class Activity:
 Use
Flip cards to demonstrate
binary addition.
 Also use the hats to show the place
values.
Binary Numbers Worksheet

Now that we know how to count in base 2,
fill in the missing binary numbers in the
middle column of the worksheet.
Binary to Decimal
1 0 0 1 0 1
1 x 20 = 1 x one
0 x 21 = 0 x two
1 x 22 = 1 x four
=
=
=
1
0
4
0 x 23 = 0 x eight
0 x 24 = 0 x sixteen
=
=
0
0
1 x 25 = 1 x thirty-two = 32
37
Back of the Worksheet

Complete the top half of the back of the
worksheet to demonstrate your
understanding of how binary and decimal
numbers relate to each other.
1111




What does this binary number represent in base
10?
Answer: 15
Notice that this is the same as the base of 2 raised
by the number of bits minus 1.
Formula
largest number = 2(n) – 1
where n represents the number of bits that are available.

So what then are the largest numbers that can be
represented using 16 bits? 32 bits? and 64 bits?
Summary
Recognize that computers, regardless of
brand or type, are binary machines.
 All the math done inside a computer is done
in binary.
 The computer converts the numbers into
decimal only when it has to display the
number on the screen or show the number
on a printed report.

End Day 1