1. Chapter 01 Numbers

2. Chapter 02 Base 10 example Decimal Number 9 7 0 1 Place 4 3 2 1 Place - 1 3 2 1 0 10 (place - 1) 10 3 10 2 10 1 10 0 =============================== = 9*1000 + 7*100 + 0*10 + 1*1 = 9701

3. Chapter 03 Numeric Values –The numeric value (expressed in base 10) of a set of digits is determined as: The sum of the products of each digit and its corresponding place value, where the place value is the numeric-base raised to the place - 1.

4. Chapter 04 Base 2 example Binary Number 0 1 0 1 2 (place - 1) 2 3 2 2 2 1 2 0 =============================== = 0*8 + 1*4 + 0*2 + 1*1 = 5

5. Chapter 05 A general example Base n Number 0 1 0 1 n (place - 1) n 3 n 2 n 1 n 0 =============================== 0*( n * n * n ) + 1*( n * n ) + 0* n + 1*1

6. Chapter 06 Commonly Used Systems Binary Base 2 OctalBase 8 DecimalBase 10 HexadecimalBase 16

7. Chapter 07 Legal Digits What are the legal digits? Starts at zero and stops at the base - 1 Binary 0, 1 Octal 0, 1, 2, 3, 4, 5, 6, 7 Decimal 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Hex 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

8. Chapter 08 What is the decimal value of? 10101 base 2 10101 base 8 10101 base 10 10101 base 16

9. Chapter 09 Binary Octal Decimal Hex 00000000000 00001010101 00010020202 00011030303 00100040404 00101050505 00110060606 00111070707 01000100808 01001110909 0101012100A 0101113110B 0110014120C 0110115130D 0111016140E 0111117150F 10000201610 10001211811 Counting in Binary, Octal, Decimal and Hexadecimal When you reach the maximum digit in a column you start over with a zero and carry a 1 into the next column to the left

10. Chapter 010 Hex = Binary Shorthand Hexadecimals are often used as a shorthand for large binary values. This shorthand is useful for specifying memory locations, e.g. Decimal - 16,274,482 Binary - 111110000101010000110010 Hex - F85432

11. Chapter 011 Binary to Hex Each Hexadecimal digit represents four binary digits 1111 1000 0101 0100 0011 0010 F 8 5 4 3 2

12. Chapter 012 Binary to Octal Each Octal digit represents three binary digits 111 110 000 101 010 000 110 010 7 6 0 5 2 0 6 2

13. Converting a decimal number to a base 2 number 1.Determine the power of two that is just smaller than the number that you want to convert. 2.You will need 1 of this power. 3.Subtract the value of this power of two from the number that you are converting. 4.Use the reminder and repeat the process starting at step 1 until the remainder is zero. 5.Put zeros in whenever you “skip” a power of 2. Chapter 013

14. Convert 235 decimal to binary Powers of 2 = 256, 128, 64, 32, 16, 8, 4, 2, 1 –You will need 1 of the 128s –You now know that this will need 8 binary digits. –Your partial answer is 1??????? –The 1 in the 8 th column represents 128 items –235 – 128 = 107 You have 107 items left to represent Chapter 014

15. Convert 235 decimal to binary Powers of 2 = 256, 128, 64, 32, 16, 8, 4, 2, 1 –You have 107 items left to represent –You will need 1 of the 64s –Your partial answer is 11?????? –The 1 in the 7 th column represents 64 items –235 – 128 – 64 = 43 –You have 43 items left to represent Chapter 015

16. Convert 235 decimal to binary Powers of 2 = 256, 128, 64, 32, 16, 8, 4, 2, 1 –You have 43 items left to represent –You will need 1 of the 32s –Your partial answer is 111????? –The 1 in the 6 th column represents 32 items –235 – 128 – 64 - 32 = 11 –You have 11 items left to represent Chapter 016

17. Convert 235 decimal to binary Powers of 2 = 256, 128, 64, 32, 16, 8, 4, 2, 1 –You have 11 items left to represent –You will need 0 of the 16s –Your partial answer is 1110???? –The 0 in the 5 th column represents 0 items –235 – 128 – 64 - 32 - 0 = 11 –You still have 11 items left to represent Chapter 017

18. Convert 235 decimal to binary Powers of 2 = 256, 128, 64, 32, 16, 8, 4, 2, 1 –You have 11 items left to represent –You will need 1 of the 8s –Your partial answer is 11101??? –The 1 in the 4 th column represents 8 items –235 – 128 – 64 - 32 - 0 – 8 = 3 –You still have 3 items left to represent Chapter 018

19. Convert 235 decimal to binary Powers of 2 = 256, 128, 64, 32, 16, 8, 4, 2, 1 –You have 3 items left to represent –You will need 0 of the 4s –Your partial answer is 111010?? –The 0 in the 3 rd column represents 0 items –235 – 128 – 64 - 32 - 0 – 8 – 0 = 3 –You still have 3 items left to represent Chapter 019

20. Convert 235 decimal to binary Powers of 2 = 256, 128, 64, 32, 16, 8, 4, 2, 1 –You have 3 items left to represent –You will need 1 of the 2s –Your partial answer is 1110101? –The 1 in the 2 nd column represents 2 items –235 – 128 – 64 - 32 - 0 – 8 – 0 – 2 = 1 –You still have 1 item left to represent Chapter 020

21. Convert 235 decimal to binary Powers of 2 = 256, 128, 64, 32, 16, 8, 4, 2, 1 –You have 1 item left to represent –You will need 1 of the 1s –Your final answer is 11101011 –The 1 in the 1 st column represents 1 item –235 – 128 – 64 - 32 - 0 – 8 – 0 – 2 – 1 = 0 –You 0 items left to represent, if you were not in the rightmost column you would fill in zeros for the remaining columns to the right. Chapter 021