Number Bases and Representation

Denary Number System (Base 10) Our number system uses 10 digits (0-9) As you move from right to left each number is worth 10 times more than the previous one E.g. 583 Base 10 means we use 10 digits and the multiplier is 10 as we move from right to left 3x18x105x100

Binary Number System (Base 2) Binary uses 2 digits (0-1) and each digit is worth twice as much as the one on its right E.g and 1 represent the on off state of electrical circuits but are inconvenient as even small numbers require a lot of digits to represent them 1x11x20x40x81x = 19

Hexadecimal Number System (Base 16) By putting binary numbers into groups of 4 bits and displaying as hexadecimal you reduce the number of digits that need to be displayed Hexadecimal uses shorthand notation to represent binary digit patterns. Digits 0-9 and letters A-f DenaryBinaryHexadecimal A B C D E F

Translating Denary to Binary E.g. translate 179 to Binary Step 1: Write down headings shown:

Translating Denary to Binary E.g. translate 179 to Binary Step 2: 128 is the largest number to go into 179, so put a 1 under

Translating Denary to Binary E.g. translate 179 to Binary Step 3: 179 – 128 = is the next largest number to go into 51, so put a 1 under

Translating Denary to Binary E.g. translate 179 to Binary Step 4: 51 – 32 = is the next largest number to go into 19, so put a 1 under

Translating Denary to Binary E.g. translate 179 to Binary Step 5: 19 – 16 = 3. 2 is the next largest number to go into 3, so put a 1 under

Translating Denary to Binary E.g. translate 179 to Binary Step 6: 3 – 2 = 1. 1 is the next largest number to go into 1, so put a 1 under

Translating Denary to Binary E.g. translate 179 to Binary Step 7: Fill in the gaps with

Translating Denary to Binary Therefore 179 in Binary is

Converting Denary to Hexadecimal Step 1: Convert Denary to Binary To convert 179 to Hexadecimal you must first convert it to Binary (as shown before) 179 in Binary = Step 2: Break the binary number into two groups of

Converting Binary to Hexadecimal Step 3: Convert blocks of 4 to hexadecimal = = B3 DenaryBinaryHexadecimal A B C D E F B 3

Task Translate 124 to Binary and Hexadecimal Translate 15 to Binary and Hexadecimal Translate 258 to Binary and Hexadecimal

Hexadecimal to Binary 92 in Hexadecimal 9 = = DenaryBinaryHexadecimal A B C D E F

Binary to Denary Converting to denary: Step 1: Put in numbers above binary number Step 2: Add up the numbers with a 1 underneath = 146 Hexadecimal 92 Binary Denary 146

Task 1.Translate Binary to Denary and to Hexadecimal 2.The ASCII code for the letter N is Show how this would be represented in Denary and Hexadecimal 3. Convert the Hexadecimal E2 to Binary and Decimal