1. Number Bases and Representation

2. 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

3. 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. 10011 0 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 1x11x20x40x81x16 ++++= 19

4. 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 111 2102 3113 41004 51015 61106 71117 810008 910019 101010A 111011B 121100C 131101D 141110E 151111F 161000010

5. Translating Denary to Binary E.g. translate 179 to Binary Step 1: Write down headings shown: 1286432168421

6. 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 128 1286432168421 1

7. Translating Denary to Binary E.g. translate 179 to Binary Step 3: 179 – 128 = 51. 32 is the next largest number to go into 51, so put a 1 under 32 1286432168421 1 1

8. Translating Denary to Binary E.g. translate 179 to Binary Step 4: 51 – 32 = 19. 16 is the next largest number to go into 19, so put a 1 under 16 1286432168421 1 1 1

9. 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 2 1286432168421 1 1 11

10. 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 1 1286432168421 1 1 11 1

11. Translating Denary to Binary E.g. translate 179 to Binary Step 7: Fill in the gaps with 0 1286432168421 10 1 1001 1

12. Translating Denary to Binary Therefore 179 in Binary is 10110011

13. 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 = 10110011 Step 2: Break the binary number into two groups of 4 1011 0011

14. Converting Binary to Hexadecimal Step 3: Convert blocks of 4 to hexadecimal 1011 0011 179 = 10110011 = B3 DenaryBinaryHexadecimal 111 2102 3113 41004 51015 61106 71117 810008 910019 101010A 111011B 121100C 131101D 141110E 151111F 161000010 B 3

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

16. Hexadecimal to Binary 92 in Hexadecimal 9 = 1001 2 = 0010 1001 0010 DenaryBinaryHexadecimal 111 2102 3113 41004 51015 61106 71117 810008 910019 101010A 111011B 121100C 131101D 141110E 151111F 161000010

17. Binary to Denary Converting 1001 0010 to denary: Step 1: Put in numbers above binary number 1286432168421 1001 0010 Step 2: Add up the numbers with a 1 underneath 128+16+2 = 146 Hexadecimal 92 Binary 10010010 Denary 146

18. Task 1.Translate Binary 0110 1110 to Denary and to Hexadecimal 2.The ASCII code for the letter N is 0100 1110. Show how this would be represented in Denary and Hexadecimal 3. Convert the Hexadecimal E2 to Binary and Decimal