Boolean Logic + Binary Arithmetic + Character Encoding + Units of Information + Number Bases

What are the gates and symbols for Boolean logic?

• AND (.) = square with curve

• OR (+) = curved triangle 

• XOR (+ with circle) = curved triangle with extra line

• Not (line on top) = triangle with circle on the end

How to create an XOR gate with only AND, OR and NOT?

From A and B, there are two AND gates, with NOT A and B + A and NOT B, which join up to an OR gate

What happens in a binary shift left?

The number doubles

What happens in a binary shift right?

The number halves and is rounded each time

How to multiply a binary number by 8 by shifting bits?

 Apply a binary shift there places to the left on the value

What are the prefixes and what do they represent?

 Kilo, mega, giga, tera, peta, gogol (10^3 + 3…)

In binary, what does each place value represent?

(2^1 +1….) 1, 2, 4,8, 16, 32, 64, 128, 256

What do the letters represent in Hexadecimal?

A10 B11 C12 D13 E14 F15

How can you convert a 2-digit Hexadecimal number into denary?

4C = (4x16) +12 = 76

What are the advantages of using Hexadecimal to binary ?

• Less difficult to work out for humans/ easier for people to read than binary

• Shorter and takes less time to type/write (not for computer)

• Any binary number can be represented in hexadecimal

• Hexadecimal is more compact when displayed on screen

What is the largest 2-digit Hexadecimal number?

FF

What’s the largest decimal number that can be represented using 5 bits?

• 6 bits = 32

• 32 -1 = 31

What are the types of character encoding and how many bits?

• ASCII = 7-bit (128 chars)

• Extended-ASCII = 8-bit (256)

• Unicode = 2^24 (over 16 million)

What are the advantages of Unicode to ASCII?

• ASCII only has 128 characters, Unicode has many more

• Character used in scientific, mathematical, technical, specialist documents

• ASCII only represents characters in the Latin alphabet, Unicode represents many more alphabets (grouped by alphabets

What is the disadvantage of Unicode to ASCII?

 Uses more bits to represent each character so takes up more bits in memory than ASCII

Facts about ASCII

• Stores each character code in 7-bits

• ASCII can represent letters in upper and lower case

• ASCII is the same in Unicode

• Character codes in ASCII and grouped together and run in sequence

What are the possible limitations of using the ASCII character set for global communication?

• Since doesn’t represent character from other alphabets 

• Communication would be limited to using the English alphabet creating a language barrier