Decimal numbers, converting

To convert 1001 into a decimal number we have to take 1 x 8 plus 0 x 4 plus 0x2 plus 1 X 1 which is 9 (decimal). Conversion of 3265 into binary is a little more difficult the largest binary number near 3265 is 2048 (or 2") and there is only one of them with 1217 left over the next largest binary number is 1024 (or 2 °), leaving 193 the next binary number is 128 (or 2 ) and then 64 (2 ) and 1 (2°). Thus, the binary equivalent of 3265 is 110011000001. 

To convert a decimal number into binary, it is necessary to look at the powers of 2 as described in Figure 42.3. Decimal numbers corresponding to ascending powers of 2 are shown here, up to 2 . Each number is just twice the previous one. 

P robiem 6. Convert a decimal number (3 4 8 9 2)wto its octal equivalent. Solution. 

Problem 7. Convert (6 5 3 4 2)s octal number to its equivalent decimal number. 

As shown above, total 16 digits are used in hexadecimal system. While converting decimal number to hexadecimal number, we divide decimal number by 16 unless we get remainder less than 16 because the base of hexadecimal system is 16. This can be understood by the following problem. 

Problem 9. Convert (5 7 A C 2)l6 hexadecimal number to decimal number. 

Hexadecimal to binary conversion. The conversion of hexadecimal to binary number is very simple just by converting each digit of hexadecimal to its binary equivalent. To make it simpler, let us know the binary equivalent of each decimal number from 0 to 15 as shown in table-1. 

Anyone who has used graph paper to plot out characters, then tediously converted the rows into decimal numbers can appreciate a character editor. Instead of drawing and erasing on paper, you can draw your characters freehand with a joystick. "Ultrafont -I-" has been written to offer almost every conceivable aid to help you design whole character sets. 

Because binary numbers contain only Is and Os, and the Os equal 0 no matter what position they re in, you really only have to worry about the Is. When trying to convert a binary number, such as 10001001, to a decimal number, all you need to do is look at the positions of the Is. As in base 10, you read the digits from MSB (left) to LSB (right). In this number, you have Is in the V, 1 , and 2° positions, which means you have decimal values of 1x128, 1x8, and 1x1, respectively. When you add these numbers together, you get the decimal equivalent 137. 

Windows comes with a tool that can help you convert decimal numbers to hex or binary numbers and back again. That tool is the Windows Calculator. When set to scientific mode, it is a great tool for doing the conversions. 

To convert a decimal number to binary, start by running Calculator in Windows 9xyou can find it on the Start menu s Accessories folder. Set it to scientific mode by going to the View menu and selecting Scientific. Then, in the Calculator s display box, type in the decimal number you want to convert. To convert the number to binary, click the button next to the word Binary. To convert it to hex, just click the button next to Hex. 

For example, if you have the binary number 01001101 (decimal number 77), you would break this 8-bit word into two groups. The first group (0100) would translate to 4 in hex, and the second group (1101) translates to D. So, this 8-bit binary number would convert to the two-digit hex number 4D. A 32-bit binary number like 01001010010010100001110000101101 converts to 4A4A1C2D (a much shorter number, in terms of the number of digits used to represent it). 

So, running them together in the right order, you get 0100101011001001 as the binary conversion. To convert to decimal, you convert that 16-bit binary number into decimal as described earlier and you will come up with the decimal number 19145. 

To convert 1001 Into a decimal number we have to take 1x8 plus 0x4 plus 0x2 plus 1x1 which is 9 (decimal). Conversion of 3265 into binary is a little more difficult the largest binary number near 3265 is 2048... 

One way to find the smallest ratio is to convert each ratio into a fraction, with the number of males as the numerator. Convert the fractions into decimal numbers, which are easier to compare to determine the smallest number. 

Convert the following ordinary decimal numbers to scientific notation. 

Convert the following numbers expressed in scientific notation to ordinary decimal numbers. 

Convert the percent natural abundance of each Isotope into a decimal number by dividing each by 100%. 

Dividing each decimal number by the smaller number, 3.727 moles, converts each to a whole number. The empirical formula is ... 

Convert llUOl I in tlie binary sysleiii to a decimal number. 

Convert each of the following decimal numbers to its binary equivalent. 

Convert each of the decimal numbers in Problem 4-1 into binary-coded-decimal (BCD) numbers. 

By how many places must the decimal point be moved, and in which direction, to convert each of the following to "ordinary" decimal numbers ... 

This number is the coefficient part of the notation. The exponent part is simply the number of places you moved the decimal point. For example, to convert the decimal number 45,000 to scientific notation, move the decimal point four places to the left to get a number between 1 and 9.999... ... 

We are accustomed to computation in the decimal system, but this need not be so. Computers, for instance, are based on a binary system, the binary numbers being 0 and 1. Digitalization of an analog signal is nothing more than the conversion of an electric potential to such a number. In Table 3-3, some decimal numbers are converted into digital numbers. 

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