Appendix E Number Systems (on (Web hosting rating) CD) 1363 Positional
Appendix E Number Systems (on CD) 1363 Positional values: 64 32 16 8 4 2 1 Then we discard the column with positional value 64 leaving: Positional values: 32 16 8 4 2 1 Next we work from the leftmost column to the right. We divide 32 into 57 and observe that there is one 32 in 57 with a remainder of 25, so we write 1 in the 32 column. We divide 16 into 25 and observe that there is one 16 in 25 with a remainder of 9 and write 1 in the 16 column. We divide 8 into 9 and observe that there is one 8 in 9 with a remainder of 1. The next two columns each produce quotients of zero when their positional values are divided into 1 so we write 0s in the 4 and 2 columns. Finally, 1 into 1 is 1 so we write 1 in the 1 column. This yields: Positional values: 32 16 8 4 Symbol values: 1 1 1 0 2 0 1 1 and thus decimal 57 is equivalent to binary 111001. To convert decimal 103 to octal, we begin by writing the positional values of the columns until we reach a column whose positional value is greater than the decimal number. We do not need that column, so we discard it. Thus, we first write: Positional values: 51264 8 1 Then we discard the column with positional value 512, yielding: Positional values: 648 1 Next we work from the leftmost column to the right. We divide 64 into 103 and observe that there is one 64 in 103 with a remainder of 39, so we write 1 in the 64 column. We divide 8 into 39 and observe that there are four 8s in 39 with a remainder of 7 and write 4 in the 8 column. Finally, we divide 1 into 7 and observe that there are seven 1s in 7 with no remainder so we write 7 in the 1 column. This yields: Positional values: 648 1 Symbol values: 147 and thus decimal 103 is equivalent to octal 147. To convert decimal 375 to hexadecimal, we begin by writing the positional values of the columns until we reach a column whose positional value is greater than the decimal number. We do not need that column, so we discard it. Thus, we first write Positional values: 4096 256 16 1 Then we discard the column with positional value 4096, yielding: Positional values: 25616 1 Next we work from the leftmost column to the right. We divide 256 into 375 and observe that there is one 256 in 375 with a remainder of 119, so we write 1 in the 256 column. We divide 16 into 119 and observe that there are seven 16s in 119 with a remainder of 7 and write 7 in the 16 column. Finally, we divide 1 into 7 and observe that there are seven 1s in 7 with no remainder so we write 7 in the 1 column. This yields:
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