Aims

• Understand the different units of data and convert between them

• Understand the need for different numbering systems in Computer Science

• Convert between denary numbers, binary numbers, hexadecimal values and binary coded decimal values

Data in computer systems is stored in binary form 1’s and 0’s

“Bit” (Binary Digit) is the smallest unit of data and is either a 1 or 0 (true or false respectively)

“Nibble” is half a byte and therefore 4 bits - remember 2 nibbles make a byte!

“Byte” contains 8 bits

There are two types of prefixes to be used when calculating size of data: Binary (Base-2) and Decimal (Base-10)

SI (Systems International) units - easier for non experts to remember

2005 IEEE (Institute of electrical and electronic engineers) binary prefix became standard for accurate storage size

Binary Prefix (Base-2): each level is based on powers of 2

Decimal Prefix (Base-10): each level is based on powers of 10

E.g. Bits to Gigabytes X/8=Bits to Bytes=/1000=XKilobytes/1000=XMegabytes/1000=Gigabytes

E.g. Gibibytes to bits X*1024=XMebibytes*1024=XKibibytes*1024=XBytes*8=Bits

When converting be careful of Prefixes!

Number Systems

Denary - Base 10- Numbers 0-9 - works from right to left moving up in units of 10

Binary - Base 2 - Used in computers as they’re made up of circuits and switches (electricity) that are either 1 (on) or 0 (off) - works right to left doubling in value 128/64/32/16/8/4/2/1

No way to know for certain what a particular pattern of bits represents until you interpret the data, same binary code could be interpreted as ASCII/pixel amount/wavelength etc.

Binary to Denary - 173

Denary to Binary - 98

Start from biggest number equal to or lower than Denary and enter 1, if higher enter 0, check by adding up numbers at the end

Hexadecimal

• Base 16Numbers 0-9 Letters A-F

• Shorthand for binary therefore faster and easier to convert to/from

• fewer mistakes as its 2 digits - each digit is 4 bits

• commonly used in colour codes RGB, assembly line programs, error codes and memory dumps

Binary to Hexadecimal

Split binary into groups of 4 bits, convert into denary and convert to Hex using table

e.g 10011111 is 9F in hexadecimal

Binary Coded Decimal

BCD form of binary system that uses 4 bits to represent a denary digit

denary converted individually into binary

Four bits used to represent 0-9 (easier to read)

Compared to binary - less efficient use of memory as 4 bits used to store each denary value

But useful when precision is crucial & easier to convert to Denary making it easier for display devices i.e clocks and calculators (as they don’t code well using binary numbers)

Converting Denary/Binary/Hexadecimal

Tip - easier to convert denary to binary then hexadecimal

Convert each Nibble into Hexidecimal - remember the Hexadecimal digits are separate e.g 6 and 4 not sixty four

To reverse Hexadecimal into Denary flip the table - A=10, sort it into Binary using Nibble then add all the binary up to make Denary