Number Systems

Decimal Numbers Decimal stands for 10 Decimal is the base 10 Number System It has 10 unique symbols 0 1 2 3 4 5 6 7 8 9 The largest symbol is the base – 1 10 – 1 = 9 9 is the largest symbol in Decimal numbers

Decimal Numbers 1000 100 10 units 4 3 5 6 4000 300 50 + 6 435610

Decimal Numbers Weight origin 103 102 101 100 Weights 1000 100 10 1 Number MSD 6 3 6 4 LSD 6000 300 60 + 4 636410

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

Binary Numbers Weight origin 23 22 21 20 Weights 8 4 2 1 2 + 1 1110

Counting in Binary Weight 8 4 2 1 decimal 0 0 0 0 0 0 0 0 1 1 0 0 1 0 2 0 0 1 1 3 0 1 0 0 4 0 1 0 1 5 0 1 1 0 6 0 1 1 1 7 1 0 0 0 8 1 0 0 1 9 1 0 1 0 10 1 0 1 1 11 1 1 0 0 12 1 1 0 1 13 1 1 1 0 14 1 1 1 1 15

Converting from Decimal to Binary The decimal number 55 = ____ In binary 55 ÷ 2 = 27.5* 1 LSB 27 ÷ 2 = 13.5 1 13 ÷ 2 = 6.5 1 6 ÷ 2 = 3.0 0 3 ÷ 2 = 1.5 1 1 ÷ 2 = 0.5 1 MSB 110111 = 5510 * If the remainder is .5 place a 1 to the right. If 0 place 0 to right

Octal Number System Octal stands for Eight Octal is the base 8 Number System It has 8 unique symbols 0 1 2 3 4 5 6 7 The largest symbol is the base – 1 8 – 1 = 7 7 is the largest symbol in the Octal number system

Octal Number System Weight origin 83 82 81 80 Weights 512 64 8 1 1024 64 48 + 7 114310

Hexadecimal Number System Hex = 6 and Decimal = 10 6+10 = 16 Hex is the base 16 Number System It has 16 symbols 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 It must have 16 UNIQUE Symbols 0 1 2 3 4 5 6 7 8 9 A B C D E F The largest symbol is 16 – 1 = 15 or F

Hexadecimal Number System Weight origin 163 162 161 160 Weights 4096 256 16 1 Number 1 2 A F 16 4096 512 160 + 15 478310

Octal Conversions The largest symbol in Octal is 7 It requires three binary bit to represent the number 7  1112 To convert a binary number to Octal, start with the LSB and mark off groups of 3. 101011010010 LSB 101-011-010-010 Write Octal symbol below 5 3 2 28

Octal Conversions To convert an Octal number to binary: Write the three bit binary equivalent below 1 5 6 48 001 101 110 100 = 11011101002 Leading zeros can be left off.

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. 1011001110101110LSB 1011-0011-1010-1110 Write Hex symbols below B 3 A E 16

Convert Hex to Binary To convert Hex to Binary, write the 4 bit Binary equivalent below each Hex digit. A 6 3 F 16 1010 0110 0011 1111 = 10100110001111112