Lecture+13

# Inthiscaserecallthat 10inbinaryequals2 indecimal

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Unformatted text preview: Binary Number to Decimal 64 26 32 25 16 24 8 23 4 22 2 21 1 20 01011001 1- 27 2- 89 3- 67 4- 79 64 + 16 + 8 + 1 = 65 128 27 Convert the Binary Number to Convert the Binary Number to Decimal 64 26 32 25 16 24 8 23 4 22 2 21 1 20 01101011 1- 85 2- 101 3- 97 4- 107 128 27 Convert the Binary Number to Convert the Binary Number to Decimal 64 26 32 25 16 24 8 23 4 22 2 21 1 20 01101011 1- 85 2- 101 3- 97 4- 107 64 + 32 + 8 + 2 + 1 = 107 Adding Binary Numbers Adding Binary Numbers 0 1 1 0 0 0 1 1 1 0 + Adding Binary Numbers Adding Binary Numbers 0 1 1 0 0 + 0 1 1 1 0 0 numbers are added column by column Adding Binary Numbers Adding Binary Numbers 0 1 1 0 0 + 0 1 1 1 0 1 0 numbers are added column by column Adding Binary Numbers Adding Binary Numbers 0 1 1 0 0 + 0 1 1 1 0 2 1 0 2 is not a valid binary digit. In this case recall that 10 in binary equals 2 in decimal Adding Binary Numbers Adding Binary Numbers 1 0 1 1 0 0 + 0 1 1 1 0 0 1 0 So we replace the 2 by a 0 and carry the extra 1. Adding Binary Numbers Adding Binary Numbers 1 0 1 1 0 0 + 0 1 1 1 0 0 1 0 Now what do we do with 1 + 1 + 1? Recall that 11 in binary equals 3 in decimal Adding Binary Numbers Adding Binary Numbers 1 1 0 1 1 0 0 + 0 1 1 1 0 1 0 1 0 So we output a 1 and carry the extra 1. Adding Binary Numbers Adding Binary Numbers 1 1 0 1 1 0 0 + 0 1 1 1 0 1 1 0 1 0 (8 + 4 = (8 + 4 + 2 = (16 + 8 + 2 = 12) 14) 26) Add the Binary Numbers Add the Binary Nu...
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