numeral representations - What are the reasons for and

Floating Point Numbers - Computerphile Extracting Speed Spectrum Hidden Data From Digital Media Decimal to IEEE 754 Floating Point Representation Crypto Technology is More Than a Currency - Bitcoin Floating Point Number Representation - Conversion Example

Yes, there is an implicitly "hidden" bit, so if your mantissa is 1100000000000000000000, then that corresponds to the base 2 number 1.11. Now, if you want to compute the value of .11 part, you just do the same thing as you would do to convert a normal binary number to decimal: multiply each bit by a power of 2. In binary that means the mantissa must be "1". Since the mantissa of a normalized binary floating point number is always 1, we don't need to store the 1. The first mantissa bit is hidden in the sense that it always exists, but we don't actually store the bit, because we know its value is 1. The DEC PDP-10 had the same mantissa with "hidden 1 bit", offset binary exponent to the left of the mantissa, but when the numbers were negative, the PDP-10 represented that value as the 2's complement of the positive value. So there was no "-0" representation (just one 0) and the integer compare operation worked in any case. Rest bits are mantissa and the actual floating point number is 1.mantissa x 2^exponent where 1.mantissa is in binary. So our numbers are 1.00101010100101110110001 x 2^-2 and 1.01000101100001011100001 x 2^6 I suggest you use Wikipedia it has a very big section on floating point representation. Much more then we can explain here to you. \$\endgroup\$ – Oldfart Apr 25 '18 at 9:50 \$\begingroup\$ Preface it by the "hidden bit" unless the exponent is 0. \$\endgroup\$ – Brian Drummond Apr 25 '18 at 9:53

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Floating Point Numbers - Computerphile

Rápido tutorial de conversão de um número decimal em ponto flutuante pra um número binário, seguido de uma conversão pro padrão IEEE-754. Why can't floating point do money? It's a brilliant solution for speed of calculations in the computer, but how and why does moving the decimal point (well, in this case binary or radix point ... note: at 3:39 Mike mentions a Bitcoin is mined every ten minutes when it is actually a block that is mined every ten minutes, at time of recording a successful block generates 12.5 new Bitcoins. Bitcoin Cryptocurrency Crash Course with Andreas Antonopoulos - Jefferson Club Dinner Meetup - Duration: 1:12:22. Jefferson Club Silicon Valley 192,861 views 1:12:22 Floating Point Numbers - Computerphile - Duration: 9:16. Computerphile Recommended for you. 9:16. Il complemento a 2 di un numero - Duration: 4:13. Agostino Perna 32,940 views.

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