CCS103 Bits, Bytes, Binary

S
CSC 103
Bits & Bytes
The Language of Computers

Bits & Bytes
 Data on a computer is represented
(and stored) as bits and bytes
 Data can be translated to display
text, numbers and pixels

Binary Language
 The language of computers is binary.
 Uses series of 1’s and 0’s –
which represent on/off state.
 Used for giving instructions
 Also used for measuring quantity
(file size/storage)

Quick History of Binary
 Morse Code (in 1844) was sent with
electrical impulses over a wire which
translated to dots and dashes (a form of
binary code) to create messages
heard by the human ear.
 Evolved into telegraph/telegram messages.

Binary Digit (Bit)
 1’s and 0’s are binary digits
 Bit is short for binary digit
 1 bit can only be 1 or 0…
so it is expanded to 8 bits
or 1 byte (28) which allows
for 256 combinations
of 1’s and 0’s

Binary Combinations
Combinations will continue to double
512, 1024, 2048…

1 Byte = 8 Bit
 8 bits or 1 Byte represents enough
numbers to convert to ASCII letters
(or characters) of the alphabet.
 For example:
The character “k” in binary is 01101011
- referenced by the number 107.
-- see chart on next slide --

Bits translated to Numbers
 Binary can represent numbers
higher than 0 and 1.
 Instead of 1’s, 10’s, 100’s, 1000’s etc.,
like our base 10 number system,
it uses binary or base 2.
 It uses 1’s, 2’s, 4’s, 8’s, 16’s, 32’s, 64’s, etc.
(starting from right (1’s) to left)

Bits converted to Numbers
4-bit example
1 0 1 1
8’s 4’s 2’s 1’s
8 + 0 + 2 + 1
8 + 3 + 1 = 11

4-bit example
1 1 1 1
8’s 4’s 2’s 1’s
8 + 4 + 2 + 1
8 + 4 + 2 + 1 = 15

4-bit example
1 0 1 0
8’s 4’s 2’s 1’s
8 + 0 + 2 + 0

4-bit example
__ __ __ __
8’s 4’s 2’s 1’s
What binary number = 9

4-bit example
1 0 0 1
8’s 4’s 2’s 1’s
8 + 0 + 0 + 1 = 9

8-bit example
1 0 1 0
8’s 4’s 2’s 1’s
128 + 0 + 32 + 0 + 8 + 0 + 2 + 0
160 + 10 = 170
1 0 1 0
128’s 64’s 32’s 16’s

8-bit example
1 1 1 1
8’s 4’s 2’s 1’s
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1
240 + 15 = 255
1 1 1 1
128’s 64’s 32’s 16’s

Shortcut to Count 8-bit
Count each side up to 15
1 1 1 1
8’s 4’s 2’s 1’s
8 + 4 + 2 + 1 8 + 4 + 2 + 1
240 + 15 = 255
1 1 1 1
128’s 64’s 32’s 16’s
15 * (1)15 * (16)

0 1 1 1
8’s 4’s 2’s 1’s
8 + 0 + 0 + 1 + 0 + 4 + 2 + 1
240 + 15 = 255
1 0 0 1
__ * (1)__ * (16)
8’s 4’s 2’s 1’s

0 1 1 1
8’s 4’s 2’s 1’s
8 + 0 + 0 + 1 + 0 + 4 + 2 + 1
151 + 7 = 158
1 0 0 1
7 * (1)9 * (16)
8’s 4’s 2’s 1’s

What binary number is 160?
0 0 0 0
8’s 4’s 2’s 1’s
0 + 0 + 0 + 0 + 0 + 0 + 0 + 0
0 + 0 = 0
0 0 0 0
__ * (1)__ * (16)
8’s 4’s 2’s 1’s

160 / 16 = _____
Remainder is the 1’s ________
__ * (1)__ * (16)

160 / 16 = 10
Remainder is the 1’s: 0
0 * (1)10 * (16)

0 0 0 0
8’s 4’s 2’s 1’s
8 + 0 + 2 + 0 + 0 + 0 + 0 + 0
160 + 0 = 160
1 0 1 0
0 * (1)10 * (16)
8’s 4’s 2’s 1’s

This is essentially the Hexadecimal System
0 0 0 0
8’s 4’s 2’s 1’s
8 + 0 + 2 + 0 + 0 + 0 + 0 + 0
160 + 0 = 160
1 0 1 0
0 * (1)10 * (16)
8’s 4’s 2’s 1’s

RGB Color translated to
Hexadecimal Color
 Hexadecimal Color is used to
describe RGB color on web pages.
For Example:
 RGB: 255 255 255
(white – highest number)
 Hex: #FF FF FF or #FFF

Hexadecimal Color
(Base 16)
 0123456789ABCDEF describes numbers
0-15 (10 is A, 11 is B, etc.)
 The first number is the number of 16’s,
the second number is the 1’s
 So, RGB number 51 would be…
 (3) 16s = 48 : first number is 3
+ (3) 1s = 3 : second number is 3
Hex = #33

So instead of…
255
Hundreds Tens Ones
Hex uses…
FF
Sixteens Ones
Hexadecimal System
(Base 16)

So, in the case of…
255
15 x 16’s = 240
15 x 1’s = 15
15 = F
15 = F
or FF240 + 15 = 255
Hexadecimal System
(Base 16)

Hexadecimal Color
(Base 16)
 What is the hexadecimal
equivalent of the RGB number
36 100 74 ?
 #___ ____ ____ ____ ____ ____
 Remember: find how many 16s and
then how many 1’s for each number.
Use letters A-F in place of 10-15.

CCS103 Bits, Bytes, Binary

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CCS103 Bits, Bytes, Binary