binary numbers

• Binary numbers can be converted to decimal numbers by multiplying the place value of each digit by its binary coefficient and adding the results.
• all computers must convert data into binary before processing
• binary is a number system where 0 means off and 1 means on
• the shortened word for binary is bits
• a bit is the smallest unit of data a computer can use to store information.
• when bits are grouped together they form larger units of data such as bytes and kilobytes
• using binary computers can store data in electronic transistors that can be turned on or off
• millions or billions of electronic transistors can fit onto a microchip
• forms of data such as text, images and/or sound must be converted to binary before it can be processed by a computer
• this process of conversion assigns a binary code to each character, pixel or sample in the data
• the resulting binary codes can then be processed through logic gates and then stored in registers
• logic gates are electronic devices that perform logical operations on binary data
• logic gates apply Boolean logic to the input values and then produce a binary output
• CPU stands for central processing unit
• registers are temporary storage areas in a computers CPU
• registers hold binary data during processing
• registers store data that need to be accessed quickly
• examples of data that registers hold are variables in a program and data being manipulated by a logic gate
• the size of a register determines how much data can be held in it at a time
• an overflow occurs when the result of a binary addition exceeds the maximum value the can be represented
• overflow occurs when the addition of 2 numbers results in a carry bit that cannot be accomodated
• to avoid overflow check the result of binary addition
• overflows can also occur using multiplication or addition
• binary shifts is the term used for multiplying or dividing in binary
• a binary shift moves all the bits in a binary number a certain number of positions to the left