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Positive floating point numbers using two bytes

Positive binary floating-point number representation using two bytes
So far, we have just considered one byte to illustrate our binary systems. One byte limits us when we need to represent real numbers. We cannot represent a wide range of numbers and we cannot represent numbers with lots of decimal places (accuracy). It’s not very common to use one byte. It is more normal to use two, four or eight bytes to represent a real number. (By convention, odd numbers of bytes are not usually used). We will now use two bytes. Remember, both the mantissa and the exponent will always be in two's complement form. This will allow us to represent both positive and negative numbers!

We will agree to have 10 bits for the mantissa. (If the left-hand bit is a 'one', then the mantissa is negative in two's complement form. If it is a 'zero' then the number is a positive 2s complement number). The remaining 6 bits will be used for the exponent. This will also be a two's complement number. (If the left-hand bit of the exponent is a 'one', the exponent is a negative 2s complement number. If it's a zero, it's a positive 2s complement number). There is absolutely no difference in the way you convert 16 bit floating-point numbers (or any other number of bits) compared to 8 bit numbers. Also, remember that the decimal point is present in the mantissa - it is there, but not part of the information given to us in the byte.

Example 11. Convert this binary number into decimal: 0110 1000 0000 0011

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