This article is picked from the article Introduction to 6811 programming.
In computers, information is represented with voltages, and it is most convenitent for he voltage level to represebt only two states:
- A binary one or binary zero
Thus computers process binary digits, or bits. For example, in an 8-bit numeral, 256 different states can be represented, since
Programmers use these 256 states to represent different things, like:
- a natural number from 0 to 255;
- an interger in the range of -128 to 127;
- a character of data(a letter, number, or printable symbol);
When programmers need to represent larger numberal, they group bytes together. A common grouping is two bytes, often called a 16-bit word, or a short(a "regular" word is 4 bytes of data). A word can have 65536 sattes, since
Decimal numbers are painful to use when talking about binary information. To make life easier, programmers started to use the base 16 hexadecimal(hex for short) numbering system whne taling about bits, bytes, and other binary data.
Hexadecimal numbers are written using the digits 0 through 9 and the letters A through F. The letters A through F represent the decimal numbers 10 through 15, respectively.
| binary | decimal | hex |
|---|---|---|
| 0b000 | 0 | 0x0 |
| 0b001 | 1 | 0x1 |
| 0b010 | 2 | 0x2 |
| 0b011 | 3 | 0x3 |
| 0b100 | 4 | 0x4 |
| 0b101 | 5 | 0x5 |
| 0b110 | 6 | 0x6 |
| 0b111 | 7 | 0x7 |
| 0b1000 | 8 | 0x8 |
| 0b1001 | 9 | 0x9 |
| 0b1010 | 10 | 0xA |
| 0b1011 | 11 | 0xB |
| 0b1100 | 12 | 0xC |
| 0b1101 | 13 | 0xD |
| 0b1110 | 14 | 0xE |
| 0b1111 | 15 | 0xF |
| 0b10000 | 16 | 0x10 |
According to table above, we can see that Binary numbers are represented by the prefix 0b. Hexadecimal numbers are represented by the prefix 0x. Decimal numbers are represented by no prefix.
Memory is oraganized as a contiguous string of addresses, or locations. The entire amount of memory that a processor can access is called its address space.
A microprocessor does its work by moving data from memory into its internal registers, processing on it, and then copying it back into memory. There are two different types of registers:
Accumulators are used to perform most arithmetic operations
Index registers are used to point at data that is located in memory
Both of these terms refer to the same thing: the program that is executed directly by the microprocessor
Machine code usually refres to the raw data stored as microprocessor's program. This is commonly described in the hexadecimal notation we've been using.
Assembly language is a set of mnemonics, or names, and a notation that is a readable yet efficient wat of writing down the machine instructions. Usually, a program taht is written in assembly language is processed by an assembler program, that converts the mnemonic instructions into machine code. The output from the assembler program is often called the object code, which can then executed directly by the microprocessor.
There are methods of representing binary numbers that are commonly used by microprocessors.
The unsigned format is used to represent numbers in the range of 0 to 255 or 0 to 65535(one word of data). But, the unsgined format has the limitation that values less than zero cannot be represented.
The signed format is used to represent numbers in the range of -128 to 127 or -32768 to 32767(one word of data). The signed format has the limitation that values greater than 127 or 32767 cannot be represented.