Chapter 16

Binary and Hexadecimal Numbers

§16.2 thru 16.3 – Addition and Subtraction of Binary Numbers

• Binary = Base 2• Addition and subtraction are similar to base 10– Can be checked using base 10 conversion– Will not learn 1’s complement method• To find 101 – 100011, find 100011 – 101 and make it

negative• Not responsible for negative answers

§16.5 – Conversion from decimal to binary

• Image on p. 530 provides the following algorithm– Changing a Number from Decimal to Binary

1. Write the number in decimal form2. Divide it by 23. Write the quotient below and the remainder to the right4. Continue this process until final quotient is 05. The binary form of the decimal number is obtained by

reading the remainders from the bottom to the top

§16.7 – Hexadecimal System

• Hexadecimal = Base 16– 16 ‘digits’ are needed: 0, 1, 2, 3, 4, ,5, 6, 7, 8, 9, A, B, C, D, E, F

• Expanded form and converting to decimal• Converting Decimal to Hexadecimal (image p. 533)

1. Write the number in decimal form2. Divide it by 163. Write the quotient below and the remainder to the right4. Continue this process until final quotient is 05. The hexadecimal form of the decimal number is obtained by

reading the remainders from the bottom to the top

§16.8 – Addition and Subtraction of Hexadecimal Numbers

• Addition and subtraction are similar to base 10– Can be checked using base 10 conversion– Will not learn complementary pairs method• To find AD – 1231, find 1231 – AD and make it negative• Not responsible for negative answers

§16.9 – Binary to Hexadecimal Conversion

• One way to convert Binary to Hex– Binary to Decimal to Hex

• Shortcut exists because 24 = 16– Every 4 digits in binary equate to one digit in hex

• Convert binary to hex• Convert hex to binary

§16.10 – Hexadecimal Code for colors

• Colors in computers are stored in hex– Primary colors: Red, Green, Blue• Red: FF0000• Green: 00FF00• Blue: 0000FF

– Colors can be made with different ‘quantities’ of Red, Green, and Blue