Inaccurate floating-point comparison attempts

The numbers 16777217.0f and 16777216.0f are Equal! WHY?
Different views of the number 16777217.0f :
f: 1.6777216E7
f: 16777216.0000000000000000000000000000000000000000
f: 0x1.0000000000000000000000000000000000000000p24

The numbers 1125899909999999.0f and 1125899906842624.0f are Equal! WHY?
Different views of the number 1125899909999999.0f :
f: 1.12589991E15
f: 1125899906842624.0000000000000000000000000000000000000000
f: 0x1.0000000000000000000000000000000000000000p50

The numbers 0x1.0p126f + 10000000000000000000000000000f and 0x1.0p126f are Equal! WHY?
Different views of the number 0x1.0p126f + 10000000000000000000000000000f :
f: 8.507059E37
f: 85070591730234620000000000000000000000.0000000000000000000000000000000000000000
f: 0x1.0000000000000000000000000000000000000000p126