This transfer is possible in two ways: direct transfer and using the decimal system.
first, let\'s make a direct transfer.
Fill in the number with missing zeros on the left
Fill in the number with missing zeros on the right
let\'s do a direct translation from binary to hexadecimal like this:
0111.1111111111111111111110002 = 0111. 1111 1111 1111 1111 1111 1000 = 0111(=7). 1111(=F) 1111(=F) 1111(=F) 1111(=F) 1111(=F) 1000(=8) = 7.FFFFF816
answer: 0111.1111111111111111111110002 = 7.FFFFF816
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
0∙23+1∙22+1∙21+1∙20+1∙2-1+1∙2-2+1∙2-3+1∙2-4+1∙2-5+1∙2-6+1∙2-7+1∙2-8+1∙2-9+1∙2-10+1∙2-11+1∙2-12+1∙2-13+1∙2-14+1∙2-15+1∙2-16+1∙2-17+1∙2-18+1∙2-19+1∙2-20+1∙2-21+0∙2-22+0∙2-23+0∙2-24 = 0∙8+1∙4+1∙2+1∙1+1∙0.5+1∙0.25+1∙0.125+1∙0.0625+1∙0.03125+1∙0.015625+1∙0.0078125+1∙0.00390625+1∙0.001953125+1∙0.0009765625+1∙0.00048828125+1∙0.000244140625+1∙0.0001220703125+1∙6.103515625E-5+1∙3.0517578125E-5+1∙1.52587890625E-5+1∙7.62939453125E-6+1∙3.814697265625E-6+1∙1.9073486328125E-6+1∙9.5367431640625E-7+1∙4.7683715820312E-7+0∙2.3841857910156E-7+0∙1.1920928955078E-7+0∙5.9604644775391E-8 = 0+4+2+1+0.5+0.25+0.125+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0.0009765625+0.00048828125+0.000244140625+0.0001220703125+6.103515625E-5+3.0517578125E-5+1.52587890625E-5+7.62939453125E-6+3.814697265625E-6+1.9073486328125E-6+9.5367431640625E-7+4.7683715820312E-7+0+0+0 = 7.9999995231628410
got It: 0111.1111111111111111111110002 =7.9999995231628410
Translate the number 7.9999995231628410 в hexadecimal like this:
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 99999952316284*16 |
F | .99999*16 |
F | .99988*16 |
F | .99805*16 |
F | .96875*16 |
F | .5*16 |
7 | .0*16 |
F | .0*16 |
F | .99999*16 |
F | .99988*16 |
F | .99805*16 |
the result of the conversion was:
7.9999995231628410 = 7.FFFFF7FFFF16
answer: 0111.1111111111111111111110002 = 7.FFFFF7FFFF16