Faint chapter in binary

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Aug 6th, 2022
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How to faint chapter in binary

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we have already completed binary addition binary subtraction and binary multiplication in this lecture we will learn binary division we want to divide 1 0 1 0 1 0 by 1 1 0 and before this binary division we will first revise division of decimal numbers we want to divide 128 by 8 so this 128 is our dividend and this 8 is our divisor we will start our division from the leftmost digit and in this case we have 1 as the leftmost digit 1 is smaller than 8 so quotient is 0 8 times 0 is 0 and 4 remainder I will subtract this 0 from 1 1 minus 0 is 1 this 2 will come down and we have 12 12 is greater than 8 so quotient is 1 I will again subtract this 8 from 12 to get the remainder remainder is 4 now this 8 will come down so we have 48 and the 8 times 6 8 times 6 will give us 48 exact division and remainder is 0 so this is our answer the quotient of this division and we have to find quotient in every division now we will move to binary division and follow the same steps we will start our division

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0b is used to tell the computer that the number you typed is a base-2 number not a base-10 number.
Only fractions with a denominator which is a power of two can be finitely represented in a binary form. For example, denominators of 0.1 (1 / 10) and 0.2 (1 / 5) are not powers of two, so these numbers cant be finitely represented in a binary format.
The number 0.1 can be represented in binary as 0.00011001100110011 .
Lets take 0.1, the first step would be converting it into a simple binary representation (multiplying the fractional part by 2 and taking the integral part) This gives me a well-known recurring binary pattern (001100110011) The final binary representation of 0.1 (up to 26-bits) is 0 .
In the above list, the first three i.e., 8421, 2421 and 5211 are Weighted Binary Codes while the other two are Non-Weighted Binary Codes.
One tenth is written in binary as 0.0[0011] where the 0011 part is repeated infinitely many times. Its not hard to see why. 1/10 is 1/2 times 1/5. The factor of 1/2 simply adds the first zero after the decimal point while 1/5 = 3/15, and 3/15 may be written as 0011/1111 which gives rise to 0.
F in binary is 1111, it represents four bits. FF is 1111 1111, which in binary represents 255. 1 = 0001 = 1 in hex 2 = 0010 = 2 in hex 9 = 1001 = 9 in hex 10 = 1010 = A in hex 11 = 1011 = B in hex 15 = 1111 = F in hex.
Computers cant store 0.1 accurately. It is stored as 0.1000000015! We explore and take a look at what is really going on.

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