Question #342587

Representation of intergers

Change the following number systems to base-10 numbers.

  • 11011010012
  • 55228
  • 12CF16
1
Expert's answer
2022-05-19T17:52:14-0400

a.


(1101101001)2=29+28+26+25+23+20(1101101001)_2=2^9+2^8+2^6+2^5+2^3+2^0

=512+256+64+32+8+1=873=512+256+64+32+8+1=873

b.


(5522)8=5(8)3+5(8)2+2(8)1+2(8)0(5522)_8=5(8)^3+5(8)^2+2(8)^1+2(8)^0

=2560+320+16+2=2898=2560+320+16+2=2898

c.


(12CF)16=1(16)3+2(16)2+12(16)1+15(16)0(12CF)_{16}=1(16)^3+2(16)^2+12(16)^1+15(16)^0

=4096+512+192+15=4815=4096+512+192+15=4815


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