*************************************** * * * * * MACHINE LANGUAGE TUTORIAL DISK * * * * WRITTEN BY DR. FIRMWARE * * * * * *************************************** The aim of this disk is for you the reader to understand machine language to an extent so that you can program fully in machine language (ml). PART I The fundamentals. The first part of the course is number bases. if you undestand binary and hexadecimal numbers and conversion between these and decimal, you can skip to the next section. Binary: Base two. Number bases are what we are dealing with here. The number base that we normally use in everday life is decimal. 'Decimal' comes from latin where it meant ten. We have ten digits, 0,1,2,3,4,5,6,7,8, and 9, which are combined in various ways to produced other numbers. It is understood that the number '345' means 3x100+4x10+5x1. The right-most digit has the least significance, while the left-most has the most significance. From left to right, the numbers that are multiplied with the digits are successive powers of 10. 1=10~0, 10=10~1, 100=10~2, etc. Now applying these fundamentals, we'll construct the base two, or binary, number system. First there are two digits, 0, and 1. So, the right-most digit has the least significance and the left-most, the most significance, just like in decimal. Now, the numbers multiplied with the digits will be successive powers of two. 2~0=1, 2~1=2, 2~2=4, 2~3=8, etc. We now have the basics down, so we'll take a number, such as '1001101', and find it's decimal value. To start, we'll take the right-most digit and find out what it is multiplied with. Since it's the right- most digit, it's multiplied with two to the power of zero. 1x2~0=1. Now, repeat the process, this time with the second right most digit, which is a 0. 0x2~1=0. Continueing produces: 1x2~2=4, 1x2~3=8, 0x2~4=0, 0x2~5=0, and 1x2~6=64. Summing the results, 1+0+4+8+0+0+64=77. So 77 is the decimal value of the binary number 1001101. If you want to practice some, just make strings of 0's and 1's and do what we did above. Conversion from decimal to binary is a little more complex. Suppose we take a decimal number, 35. To convert, we do a series of steps. 1> Divide the number by two, and put the remainder aside. 2> Replace the dividend with the quotient. 3> Repeat step 1 & 2 until the number reaches zero. 4> Take the remainders and place them in a row, the first is right-most, the last is left-most. And that's it. To demostrate, we'll convert 35 to binary. 0 R=1 ------- --- ! 2) 1 R=0 ! --- ! 2) 2 R=0 ! --- v 2) 4 R=0 100011 --- ~ 2) 8 R=1 ! --- ! 2) 17 R=1 ------------ --- 2) 35 There. Quite simple. The diagram would look somewhat better on paper, but this will have to do in the mean while. Hexadecimal 'Hex', as it is affectionately called by in most computerese dialects, is nothing more than a base sixteen number system. Let's go through some basics. It has 16 digits. These digits are the numbers 0-9, and the letters A-F. The reason why the letters are included is because there aren't enough numbers. Let's take a number, $4A. Note that when you see a '$' infront of a number, it denotes that the number is a hex number. $4A means 4x16~1+10x16~0. The letters are the numbers from 10-15, A being 10, B is 11, C=12, etc. Conversion to decimal is exactly the same as for binary. To demostrate we'll convert 10234 to hex. 0 ------ 16) 2 R=7 ---- ------ v 16) 39 R=15 7FA ------ ~ 16) 639 R=10 -----/ ------ 16) 10234 There we are! 10234 is $7FA. One interesting fact: since 16=2~4, then a 4 digit binary number is equal to 1 hex digit, i.e. 1111=$F, 1010=$A, etc. This makes binary to hex, and vice versa, conversion very easy. For example, the number $3A0 in binary is 0011 1010 0000. ~ ~ ~ ! ! $0 ! $a $3 This ends the discussion on number bases and now the reader should be aquianted with binary and hex and what they mean. Bits and Bytes. A bit is really only a binary digit. In other words, a 1 or a 0. These are digital computers handle, strings upon strigs of bits. Unfortunately, bits are very combersome, because even the charcters that you see require 8 bits each. The screen size is 40x24, and that adds up to 7680! bits! A more convinient form are two digit hex numbers. A two digit hex number represents 8 bits in only two digits. A more common name for this compact unit is a byte. You might know that your computer has 64K RAM. The K represents 1,024 bytes. So this means that your computer has 65,536 bytes of RAM memory. 65,536 can be expresses more conviniently as 2~16. This is important for reasons that we'll discuss a little later. Well, there we are! Now that we have some basics down, we can get to some machine language. ======================================= DR. FIRMWARE, OCT 21st, 1985. I CAN BE REACHED ON TESTY, 514-332-6852 OR ON TRANSFERS AE, 514-738-1247 =======================================
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