Binary01.ppt Decimal Decimal: Base 10 means 10 Unique numerical digits 0 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 101001,00010,000 Weight Positions 3, 4 6 7 10 3.

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Presentation transcript:

Binary01.ppt Decimal Decimal: Base 10 means 10 Unique numerical digits ,00010,000 Weight Positions 3, x 1000 = x 100 = x 10 = 60 7 x 1 = ,467 etc.

Binary01.ppt Decimal Addition start start Carry 1

Binary01.ppt Binary Decimal: Base 2 means 2 Unique numerical digits 0 1 On Off In Out Left Right Decimal Weight Positions 32 etc x 32 = 32 0 x 16 = 0 1 x 8 = 8 1 x 4 = 4 0 x 2 = 0 1 x 1 =

Binary01.ppt Binary Addition with a 1 carry Carry

Binary01.ppt Hexadecimal Decimal: Base 16 means 16 Unique numerical digits A B C D E F Decimal Equivalents 0 = 0 1 = 1 2 = 2 3 = 3 4 = 4 5 = 5 6 = 6 7 = 7 8 = 8 9 = 9 A = 10 B = 11 C = 12 D = 13 E = 14 F = 15

Binary01.ppt Hexadecimal 0-F 0-F 0-F 0-F 0-F 0-F 1,048,576 65,536 4, Decimal Weight Positions A 3 9 D 6 C 16 A = 10 X 1,048,576 = 10,485, = 3 X 65,536 = 196, = 9 X 4096 = 36,864 + D = 13 X 256 = 3, = 6 X 16 = 96 + C = 12 X 1 = ,722,668 10

Binary01.ppt Hexadecimal to Binary 0 = = = = = = = = = = 1001 A = 1010 B = 1011 C = 1100 D = 1101 E = 1110 F = 1111 It takes 4 bits to make one Hex number

Binary01.ppt Octal Decimal: Base 8 means 8 Unique numerical digits Decimal Equivalents 0 = 0 1 = 1 2 = 2 3 = 3 4 = 4 5 = 5 6 = 6 7 = 7 Octal to Binary 0 = = = = = = = = 111 It takes 3 bits to make one Octal number

Binary01.ppt Decimal Weight Positions Octal x 512 = 3, x 5 = 80 2 x 8 = 16 3 x 1 = ,683 10

Binary01.ppt Binary to Decimal Decimal Weights = Add the decimal weights of the “1” bits Decimal to Binary 1. Find the largest binary bit that will fit in the number without going over the number 2. Mark that bit as “on” and subtract the bit weight value from the decimal number 3. Repeat steps 1 and 2 until there are no more numbers remaining in the decimal number

Binary01.ppt Hex to Binary C 5 9 B = Convert Hex to Binary Binary to Hex Divide bits into groups of C 5 9 B

Binary01.ppt Binary to Octal Divide bits into groups of Octal to Binary

Binary01.ppt Hex to Octal to Decimal Break the hex or octal or decimal number into binary Decimal: add the weights = 2, Hexadecimal: divide the bits into patterns of 4 = B8B 16 Octal: divide the bits into patterns of 3 =