Chapter 01 Numbers

Chapter 02 Base 10 example Decimal Number Place Place (place - 1) =============================== = 9* * *10 + 1*1 = 9701

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.

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

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

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

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

Chapter 08 What is the decimal value of? base base base base 16

Chapter 09 Binary Octal Decimal Hex A B C D E F 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

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 Hex - F85432

Chapter 011 Binary to Hex Each Hexadecimal digit represents four binary digits F

Chapter 012 Binary to Octal Each Octal digit represents three binary digits

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

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

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

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 – = 11 –You have 11 items left to represent Chapter 016

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 – = 11 –You still have 11 items left to represent Chapter 017

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 – – 8 = 3 –You still have 3 items left to represent Chapter 018

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 ?? –The 0 in the 3 rd column represents 0 items –235 – 128 – – 8 – 0 = 3 –You still have 3 items left to represent Chapter 019

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 ? –The 1 in the 2 nd column represents 2 items –235 – 128 – – 8 – 0 – 2 = 1 –You still have 1 item left to represent Chapter 020

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 –The 1 in the 1 st column represents 1 item –235 – 128 – – 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