ITEC 1011 Introduction to Information Technologies 1. Number Systems Chapt. 2 Location in course textbook

ITEC 1011 Introduction to Information Technologies Common Number Systems SystemBaseSymbols Used by humans? Used in computers? Decimal100, 1, … 9YesNo Binary20, 1NoYes Octal80, 1, … 7No Hexa- decimal 160, 1, … 9, A, B, … F No

ITEC 1011 Introduction to Information Technologies Quantities/Counting (1 of 3) DecimalBinaryOctal Hexa- decimal p. 33

ITEC 1011 Introduction to Information Technologies Quantities/Counting (2 of 3) DecimalBinaryOctal Hexa- decimal A B C D E F

ITEC 1011 Introduction to Information Technologies Quantities/Counting (3 of 3) DecimalBinaryOctal Hexa- decimal Etc.

ITEC 1011 Introduction to Information Technologies Conversion Among Bases The possibilities: Hexadecimal DecimalOctal Binary pp

ITEC 1011 Introduction to Information Technologies Quick Example = = 31 8 = Base

ITEC 1011 Introduction to Information Technologies =>5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = Base Weight

ITEC 1011 Introduction to Information Technologies Binary to Decimal Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Binary to Decimal Technique –Multiply each bit by 2 n, where n is the “weight” of the bit –The weight is the position of the bit, starting from 0 on the right –Add the results

ITEC 1011 Introduction to Information Technologies Example => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = Bit “0”

ITEC 1011 Introduction to Information Technologies Octal to Decimal Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Octal to Decimal Technique –Multiply each bit by 8 n, where n is the “weight” of the bit –The weight is the position of the bit, starting from 0 on the right –Add the results

ITEC 1011 Introduction to Information Technologies Example => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 =

ITEC 1011 Introduction to Information Technologies Hexadecimal to Decimal Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Hexadecimal to Decimal Technique –Multiply each bit by 16 n, where n is the “weight” of the bit –The weight is the position of the bit, starting from 0 on the right –Add the results

ITEC 1011 Introduction to Information Technologies Example ABC 16 =>C x 16 0 = 12 x 1 = 12 B x 16 1 = 11 x 16 = 176 A x 16 2 = 10 x 256 =

ITEC 1011 Introduction to Information Technologies Decimal to Binary Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Decimal to Binary Technique –Divide by two, keep track of the remainder –First remainder is bit 0 (LSB, least-significant bit) –Second remainder is bit 1 –Etc.

ITEC 1011 Introduction to Information Technologies Example = ? =

ITEC 1011 Introduction to Information Technologies Octal to Binary Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Octal to Binary Technique –Convert each octal digit to a 3-bit equivalent binary representation

ITEC 1011 Introduction to Information Technologies Example = ? =

ITEC 1011 Introduction to Information Technologies Hexadecimal to Binary Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Hexadecimal to Binary Technique –Convert each hexadecimal digit to a 4-bit equivalent binary representation

ITEC 1011 Introduction to Information Technologies Example 10AF 16 = ? A F AF 16 =

ITEC 1011 Introduction to Information Technologies Decimal to Octal Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Decimal to Octal Technique –Divide by 8 –Keep track of the remainder

ITEC 1011 Introduction to Information Technologies Example = ? =

ITEC 1011 Introduction to Information Technologies Decimal to Hexadecimal Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Decimal to Hexadecimal Technique –Divide by 16 –Keep track of the remainder

ITEC 1011 Introduction to Information Technologies Example = ? = 4D = D

ITEC 1011 Introduction to Information Technologies Binary to Octal Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Binary to Octal Technique –Group bits in threes, starting on right –Convert to octal digits

ITEC 1011 Introduction to Information Technologies Example = ? =

ITEC 1011 Introduction to Information Technologies Binary to Hexadecimal Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Binary to Hexadecimal Technique –Group bits in fours, starting on right –Convert to hexadecimal digits

ITEC 1011 Introduction to Information Technologies Example = ? B B = 2BB 16

ITEC 1011 Introduction to Information Technologies Octal to Hexadecimal Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Octal to Hexadecimal Technique –Use binary as an intermediary

ITEC 1011 Introduction to Information Technologies Example = ? E = 23E 16

ITEC 1011 Introduction to Information Technologies Hexadecimal to Octal Hexadecimal DecimalOctal Binary

ITEC 1011 Introduction to Information Technologies Hexadecimal to Octal Technique –Use binary as an intermediary

ITEC 1011 Introduction to Information Technologies Example 1F0C 16 = ? 8 1 F 0 C F0C 16 =

ITEC 1011 Introduction to Information Technologies Exercise – Convert... Don’t use a calculator! DecimalBinaryOctal Hexa- decimal AF Skip answer Answer

ITEC 1011 Introduction to Information Technologies Binary Addition (1 of 2) Two 1-bit values pp ABA + B “two”

ITEC 1011 Introduction to Information Technologies Binary Addition (2 of 2) Two n-bit values –Add individual bits –Propagate carries –E.g.,

ITEC 1011 Introduction to Information Technologies Multiplication (1 of 3) Decimal (just for fun) pp x

ITEC 1011 Introduction to Information Technologies Multiplication (2 of 3) Binary, two 1-bit values AB A  B

ITEC 1011 Introduction to Information Technologies Multiplication (3 of 3) Binary, two n-bit values –As with decimal values –E.g., 1110 x

ITEC 1011 Introduction to Information Technologies Fractions Decimal to decimal (just for fun) pp =>4 x = x = x 10 0 =

ITEC 1011 Introduction to Information Technologies Fractions Binary to decimal pp => 1 x 2 -4 = x 2 -3 = x 2 -2 = x 2 -1 = x 2 0 = x 2 1 =

ITEC 1011 Introduction to Information Technologies Fractions Decimal to binary p x x x x x x etc

ITEC 1011 Introduction to Information Technologies Exercise – Convert... Don’t use a calculator! DecimalBinaryOctal Hexa- decimal C.82 Skip answer Answer

ITEC 1011 Introduction to Information Technologies Exercise – Convert … DecimalBinaryOctal Hexa- decimal …35.63…1D.CC… D C C.82 Answer

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