Using Binary
Using Binary
Understanding Binary
- Binary, also known as base-2, is a binary numeral system or language used by computer devices. Each digit is referred to as a bit.
- A byte is made up of 8 bits.
- Binary is used inside a computer as it works using logic gates, and it’s simpler to use a system based on two states – 1 (on) and 0 (off).
Converting Decimal to Binary
- For converting decimal to binary, start with the highest power of 2 that goes into the decimal number and work down to 2^0.
- Mark a 1 under each power of 2 that goes into the original number and 0 where it doesn’t.
- Write out these 1’s and 0’s in the same line and this is your binary number.
Converting Binary to Decimal
- For converting binary to decimal, multiply each binary digit by the corresponding power of 2.
- The rightmost bit represents 2^0, the next one to the left 2^1, then 2^2, etc.
- Sum all these products and the result will be the decimal equivalent of your binary number.
Binary Arithmetic
- Binary addition and subtraction follow similar rules as decimals.
- 0 + 0 is 0, 0 + 1 or 1 + 0 is 1, 1 + 1 is 10 (which is ‘2’ in decimal but ‘10’ in binary).
- When you add 1 + 1, the ‘1’ carried forward is added to the bits in the next column.
- In binary subtraction, borrow from the next column if the subtrahend is larger than the minuend, similar to the decimal system.
Binary Shifts
- Binary shifts involve moving all bits in a binary number to the left or right and filling the gaps with 0’s.
- A left shift multiplies a binary number by 2 and a right shift divides a number by 2 (ignoring remainders).
- They can be used for efficient multiplication or division by powers of 2.