unsigned u =10； int i = -42； cout << i+i <<endl； cout << u+i<<endl;//if int take...

unsigned u =10；
int i = -42；
cout << i+i <<endl；
cout << u+i<<endl;//if int take 32 bit, output 4294967264

I know when unsigned and singed operate together, they need to be converted, but why is the answer 4294967264? What does it have to do with int .…… 32 bit

Expert Solution

-42 in stored in memory using 2's complement
This is negative. so, follow these steps to convert this into a 2's complement binary
Step 1:
Divide 42 successively by 2 until the quotient is 0
   > 42/2 = 21, remainder is 0
   > 21/2 = 10, remainder is 1
   > 10/2 = 5, remainder is 0
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 101010
So, 42 of decimal is 101010 in binary
Adding 26 zeros on left hand side of this number to make this of length 32
So, 42 in normal binary is 00000000000000000000000000101010
Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.
   00000000000000000000000000101010 is flipped to 11111111111111111111111111010101
Step 3:. Add 1 to above result
11111111111111111111111111010101 + 1 = 11111111111111111111111111010110
so, -42 in 2's complement binary is 11111111111111111111111111010110

unsigned value of 11111111111111111111111111010110 is
=> 11111111111111111111111111010110
=> 1x2^31+1x2^30+1x2^29+1x2^28+1x2^27+1x2^26+1x2^25+1x2^24+1x2^23+1x2^22+1x2^21+1x2^20+1x2^19+1x2^18+1x2^17+1x2^16+1x2^15+1x2^14+1x2^13+1x2^12+1x2^11+1x2^10+1x2^9+1x2^8+1x2^7+1x2^6+0x2^5+1x2^4+0x2^3+1x2^2+1x2^1+0x2^0
=> 1x2147483648+1x1073741824+1x536870912+1x268435456+1x134217728+1x67108864+1x33554432+1x16777216+1x8388608+1x4194304+1x2097152+1x1048576+1x524288+1x262144+1x131072+1x65536+1x32768+1x16384+1x8192+1x4096+1x2048+1x1024+1x512+1x256+1x128+1x64+0x32+1x16+0x8+1x4+1x2+0x1
=> 2147483648+1073741824+536870912+268435456+134217728+67108864+33554432+16777216+8388608+4194304+2097152+1048576+524288+262144+131072+65536+32768+16384+8192+4096+2048+1024+512+256+128+64+0+16+0+4+2+0
=> 4294967254

so, u + i = 10 + 4294967254 = 4294967264

venereology answered 3 months ago

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