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A big problem with the binary system is verbosity. To represent the value 10 requires eight binary digits. The decimal version requires only three decimal digits and, thus, represents numbers much more compactly than does the binary numbering system. This fact was not lost on the engineers who designed binary computer systems. When dealing with large values, binary numbers quickly become too unwieldy.
Unfortunately, the computer thinks in binary, so most of the time it is convenient to use the binary numbering system. Although we can convert between decimal and binary, the conversion is not a trivial task. The hexadecimal base 16 numbering system solves these problems. Hexadecimal numbers offer the two features we're looking for: Because of this, most computer systems engineers use the hexadecimal numbering system.
Since the radix base of a hexadecimal number is 16, each hexadecimal digit to the left of the hexadecimal point represents some value times a successive power of For example, the number 16 is equal to:. Each hexadecimal digit can represent one of sixteen values between 0 and 15 Since there are only ten decimal digits, we need to invent six additional digits to represent the values in the range 10 10 through 15 Rather than create new symbols for these digits, we'll use the letters A through F.
The following are all examples of valid hexadecimal numbers:. Since we'll often need to enter hexadecimal numbers into the computer system, we'll need a different mechanism for representing hexadecimal numbers. After all, on most computer systems you cannot enter a subscript to denote the radix of the associated value. We'll adopt the following conventions:. As you can see, hexadecimal numbers are compact and easy to read. In addition, you can easily convert between hexadecimal and binary. Consider the following table:.
This table provides all the information you'll ever need to convert any hexadecimal number into a binary number or vice versa.
To convert a hexadecimal number into a binary number, simply substitute the corresponding four bits for each hexadecimal digit in the number. To convert a binary number into hexadecimal format is almost as easy. The first step is to pad the binary number with zeros to make sure that there is a multiple of four bits in the number.
For example, given the binary number , the first step would be to add two bits to the left of the number so that it contains 12 bits. The converted binary value is The next step is to separate the binary value into groups of four bits, e.
Finally, look up these binary values in the table above and substitute the appropriate hexadecimal digits, i. Contrast this with the difficulty of conversion between decimal and binary or decimal and hexadecimal! Since converting between hexadecimal and binary is an operation you will need to perform over and over again, you should take a few minutes and memorize the table above.
Even if you have a calculator that will do the conversion for you, you'll find manual conversion to be a lot faster and more convenient when converting between binary and hex. There are several operations we can perform on binary and hexadecimal numbers. For example, we can add, subtract, multiply, divide, and perform other arithmetic operations. Although you needn't become an expert at it, you should be able to, in a pinch, perform these operations manually using a piece of paper and a pencil.
Having just said that you should be able to perform these operations manually, the correct way to perform such arithmetic operations is to have a calculator that does them for you. There are several such calculators on the market; the following table lists some of the manufacturers who produce such devices:. Some manufacturers of Hexadecimal Calculators circa This list is by no means exhaustive. Other calculator manufacturers probably produce these devices as well.
The Hewlett-Packard devices are arguably the best of the bunch. However, they are more expensive than the others. If you plan on doing any assembly language programming at all, owning one of these calculators is essential. To understand why you should spend the money on a calculator, consider the following arithmetic problem:. But that is not correct! A similar problem exists with the arithmetic problem:. Remember, this problem is asking "what is the difference between sixteen and one?
Even if the two problems above don't bother you, in a stressful situation your brain will switch back into decimal mode while you're thinking about something else and you'll produce the incorrect result.
Moral of the story - if you must do an arithmetic computation using hexadecimal numbers by hand, take your time and be careful about it. Either that, or convert the numbers to decimal, perform the operation in decimal, and convert them back to hexadecimal. Many people confuse numbers and their representation. A common question beginning assembly language students have is "I've got a binary number in the EAX register, how do I convert that to a hexadecimal number in the EAX register?
Human readable forms of numeric quantities are always strings of characters. This would provide the decimal representation of the numeric quantity. It's the same number, but we've converted it to a different sequence of characters because presumably we wanted to view the number using hexadecimal representation rather than decimal. Likewise, if we want to see the number in binary, then we must convert this numeric value to a string containing a one followed by seven zeros.
By default, HLA displays all byte, word, and dword variables using the hexadecimal numbering system when you use the stdout. Consider the following program that converts values input as decimal numbers to their hexadecimal equivalents:. In a similar fashion, the default input base is also hexadecimal for registers and byte, word, or dword variables. The following program is the converse of the one above- it inputs a hexadecimal value and outputs it as decimal:.
Just because the HLA stdout. Remember, memory and registers hold numeric values, not hexadecimal or decimal values. The choice of hexadecimal vs. You could very easily modify HLA so that it outputs registers and byte , word , or dword variables as decimal values rather than as hexadecimal. If you need to print the value of a register or byte , word , or dword variable as a decimal value, simply call one of the putiX routines to do this.
Any eight-bit parameter will work. So you could pass an eight-bit register, an int8 variable, or a byte variable as the parameter to stdout. The following program demonstrates the decimal conversion program Program 3. Note that HLA's stdin.
That is, if you attempt to read an int8 , int16 , or int32 variable, the default input base is decimal. If you attempt to read a register or byte , word , or dword variable, the default input base is hexadecimal.
If you want to change the default input base to decimal when reading a register or a byte , word , or dword variable, then you can use stdin. If you want to go in the opposite direction, that is you want to input or output an int8 , int16 , or int32 variable as a hexadecimal value, you can call the stdout.
The following program demonstrates the use of a few of these routines:. Web Site Hits Since Jan 1,