Decimal to Binary NumbersMr. BrockelmanLogic Design 101

Representing Decimal Numbers in BinaryDecimal numbers have TEN unique values (0 thru 9)

Binary numbers have TWO unique values (0 and 1)

Decimal to Binary RepresentationDecimalBinary184210123456789Each additional column in a decimal number is a multiple of 10.Each additional column in a binary number is a multiple of 2.For this example we only need one column for decimal but 4 columns for an equal binary number.ColumnValue

Decimal to Binary RepresentationDecimalBinary1842100000123456789Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary Zero (0+0+0+0)

Decimal to Binary RepresentationDecimalBinary18421000001000123456789Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary One (0+0+0+1)

Decimal to Binary RepresentationDecimalBinary184210000010001200103456789Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary Two (0+0+2+0)

Decimal to Binary RepresentationDecimalBinary1842100000100012001030011456789Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary Three (0+0+2+1)

Decimal to Binary RepresentationDecimalBinary18421000001000120010300114010056789Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary Four (0+4+0+0)

Decimal to Binary RepresentationDecimalBinary184210000010001200103001140100501016789Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary Five (0+4+0+1)

Decimal to Binary RepresentationDecimalBinary1842100000100012001030011401005010160110789Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary Six (0+4+2+0)

Decimal to Binary RepresentationDecimalBinary18421000001000120010300114010050101601107011189Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary Seven (0+4+2+1)

Decimal to Binary RepresentationDecimalBinary184210000010001200103001140100501016011070111810009Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary Eight (8+0+0+0)

Decimal to Binary RepresentationDecimalBinary1842100000100012001030011401005010160110701118100091001Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)The 1s, 2s,4s, and 8s binary columns are added together to equate to a decimal number.Binary Nine (8+0+0+1)

Decimal to Binary RepresentationDecimalBinary1018421101010111011121100131101141110151111Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)For this example we need two columns for decimal and 4 columns for an equal binary number.Binary Ten (8+0+2+0)

Decimal to Binary RepresentationDecimalBinary1018421101010111011121100131101141110151111Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)For this example we need two columns for decimal and 4 columns for an equal binary number.Binary Eleven (8+0+2+1)

Decimal to Binary RepresentationDecimalBinary1018421101010111011121100131101141110151111Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)For this example we need two columns for decimal and 4 columns for an equal binary number.Binary Twelve(8+4+0+0)

Decimal to Binary RepresentationDecimalBinary1018421101010111011121100131101141110151111Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)For this example we need two columns for decimal and 4 columns for an equal binary number.Binary Thirteen(8+4+0+1)

Decimal to Binary RepresentationDecimalBinary1018421101010111011121100131101141110151111Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)For this example we need two columns for decimal and 4 columns for an equal binary number.Binary Fourteen(8+4+2+0)

Decimal to Binary RepresentationDecimalBinary1018421101010111011121100131101141110151111Binary numbers can only have a 0 (zero) or a 1 (one) as a column valueEach binary column equates to their displayed value (8, 4, 2, 1)For this example we need two columns for decimal and 4 columns for an equal binary number.Binary Fifteen(8+0+2+0)

Decimal to Binary NumbersMr. BrockelmanLogic Design 101