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 Number System Conversions Between Number System Arithematic Operations 1's & 2's Complement Gray Codes Arithmetic Circuits Logical Gates and Truth Table Funtions Boolean Expressions Boolean Algebra Karnaugh Map Multiplexer DeMultiplexer Encoder & Decoder TTL Circuits Multivibrators 555 Timer Flip Flops RS Flip - Flop JK Flip - Flop D Flip - Flop Shift Register Schmitt Trigger Asynchronous Counters Synchronous Counters Digital - Analog Conversion Data Flow ROM Memory Drives Electronics Equation Resistor Color Codes

## Number System

### Bit & Byte

Computer uses the binary system. Any physical system that can exist in two distinct states (e.g., 0-1, on-off, hi-lo, yes-no, up-down, north-south, etc.) has the potential of being used to represent numbers or characters.

A binary digit is called a bit. There are two possible states in a bit, usually expressed as 0 and 1.

A series of eight bits strung together makes a byte, much as 12 makes a dozen. With 8 bits, or 8 binary digits, there exist 2^8=256 possible combinations. The following table shows some of these combinations. ### K & M

2^10=1024 is commonly referred to as a "K". It is approximately equal to one thousand. Thus, 1 Kbyte is 1024 bytes. Likewise, 1024K is referred to as a "Meg". It is approximately equal to a million. 1 Mega byte is 1024*1024=1,048,576 bytes. If you remember that 1 byte equals one alphabetical letter, you can develop a good feel for size.

### Number System

You may regard each digit as a box that can hold a number. In the binary system, there can be only two choices for this number -- either a "0" or a "1". In the octal system, there can be eight possibilities:

"0", "1", "2", "3", "4", "5", "6", "7".

In the decimal system, there are ten different numbers that can enter the digit box:

"0", "1", "2", "3", "4", "5", "6", "7", "8", "9".

In the hexadecimal system, we allow 16 numbers:

"0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "A", "B", "C", "D", "E", and "F".

As demonstrated by the following table, there is a direct correspondence between the binary system and the octal system, with three binary digits corresponding to one octal digit. Likewise, four binary digits translate directly into one hexadecimal digit. In computer usage, hexadecimal notation is especially common because it easily replaces the binary notation, which is too long and human mistakes in transcribing the binary numbers are too easily made.