Number Systems Decimal Numbers Decimal stands for 10

Number Systems

Decimal Numbers Decimal stands for 10 Decimal is the base 10 Number System It has 10 unique symbols 0123456789 The largest symbol is the base – 1 10 – 1 = 9 9 is the largest symbol in Decimal numbers

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

Decimal Numbers Weight origin 103 102 101 100 Weights 1000 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 Weights Number 8 0 2 +1 1110 23 8 1 22 4 0 21 2 1 20 1 12

Counting in Binary Weight 8 0 0 0 0 1 1 1 1 4 0 0 0 0 1 1 1 1 2 0 0 1 1 1 0 1 0 1 decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 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 01234567 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 Weights Number 1024 64 48 + 7 114310 83 8 2 512 64 2 1 80 8 1 6 78

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 0123456789 A B C D E F The largest symbol is 16 – 1 = 15 or F

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

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 -010 -010 Write Octal symbol below 5 3 2 28

Octal Conversions To convert an Octal number to binary: Write three bit binary equivalent below 1 5 6 48 001 110 100 = 1101002 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. 1011001110101110 LSB 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