5.
00000 00001 00011 00010 00110 00111 00101 00100 01100 01101 01111 01110 01010 01011 01001 01000 11000 11001 11011 11010 11110 11111 11101 11100 10100 10101 10111 10110 10010 10011 10001 100006.
0.015625 = 0.000001 in binary
which is 1.0 with a binary exponent of -6
the mantissa representation is 23 zeros (since the 1 is not stored) and the exponent representation is 127 - 6 = 121
and the sign is negative (sign bit is 1)
so the bytes are
10111100 10000000 00000000 00000000
in Hexadecimal this is BC 80 00 00
-----------------------------------------------------------------
1.625 = 1.101 in binary (so the exponent is zero since the number is already normalised)
the mantissa representation is 1010000 00000000 00000000 and the exponent representation is 127 + 0 = 127
and the sign bit is 0
so the bytes are
00111111 11010000 00000000 00000000
in Hexadecimal .... 3F D0 00 00
-------------------------------------------------------------------
7.
43 F0 B4 00... in binary this is 01000011 11110000 10110100 00000000
The number is positive
The exponent is 135 - 127 = 8
the mantissa representation is 1110000 10110100 00000000
the number is 1.1110000101101 by 2 to the 8th
which is 111100001.01101
256 + 128 + 64 + 32 + 1 + 0.25 + 0.125 + 0.03125 = 481.40625
------------------------------------------------------------------------------------------------------
3D E8 00 00... in binary this is 00111101 11101000 00000000 00000000
The number is positive
The exponent is 123 - 127 = -4
the mantissa representation is 1101000 00000000 00000000
the number is 1.1101 by 2 to the minus 4
which is 0.00011101
0.0625
0.03125
0.015625
0.00390625
---------------
0.11328125
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