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Number Systems

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**Decimal Numbers Decimal stands for 10**

Decimal is the base 10 Number System It has 10 unique symbols The largest symbol is the base – 1 10 – 1 = 9 9 is the largest symbol in Decimal numbers

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Decimal Numbers units 4000 300 50 + 6 435610

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**Decimal Numbers Weight origin 103 102 101 100 Weights 1000 100 10 1**

Number MSD LSD 6000 300 60 + 4 636410

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**Binary Numbers Binary stands for 2 Binary is the base 2 number system**

It has two unique symbols 0 and 1 The largest symbol in Binary is the base – 1 2 – 1 = 1 1 is the largest symbol in the Binary Number system

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**Binary Numbers Weight origin 23 22 21 20 Weights 8 4 2 1**

2 + 1 1110

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Counting in Binary Weight decimal

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**Converting from Decimal to Binary**

The decimal number 55 = ____ In binary 55 ÷ 2 = 27.5* 1 LSB 27 ÷ 2 = 13 ÷ 2 = 6 ÷ 2 = 3 ÷ 2 = 1 ÷ 2 = MSB = 5510 * If the remainder is .5 place a 1 to the right. If 0 place 0 to right

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**Octal Number System Octal stands for Eight**

Octal is the base 8 Number System It has 8 unique symbols The largest symbol is the base – 1 8 – 1 = 7 7 is the largest symbol in the Octal number system

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**Octal Number System Weight origin 83 82 81 80 Weights 512 64 8 1**

1024 64 48 + 7 114310

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**Hexadecimal Number System**

Hex = 6 and Decimal = = 16 Hex is the base 16 Number System It has 16 symbols It must have 16 UNIQUE Symbols A B C D E F The largest symbol is 16 – 1 = 15 or F

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**Hexadecimal Number System**

Weight origin Weights Number A F 16 4096 512 160 + 15 478310

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**Octal Conversions The largest symbol in Octal is 7**

It requires three binary bit to represent the number 7 To convert a binary number to Octal, start with the LSB and mark off groups of 3. LSB Write Octal symbol below

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**Octal Conversions To convert an Octal number to binary:**

Write the three bit binary equivalent below = Leading zeros can be left off.

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**Convert Binary to Hex The largest symbol in Hex is 15 or F**

It requires four binary bits to represent the number 15 or the symbol F 11112 To convert a binary number to Hex, start with the LSB and mark off groups of 4. LSB Write Hex symbols below B A E 16

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Convert Hex to Binary To convert Hex to Binary, write the 4 bit Binary equivalent below each Hex digit. A F 16 =

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