Part I: Two\'s complement la. Convert unsigned binary 0101 1010 0001 1010 to dec

Question

Part I: Two's complement la. Convert unsigned binary 0101 1010 0001 1010 to decimal lb. Convert 16-bit two's complement 0101 1010 0001 1010 to decimal 1c. Do the results of#1a and #1b have the same decimal value? Why or why not? 2a. Convert unsigned bmary 1101 1010 0001 1010 to decimal 2b. Convert 16-bit two's complement bimary 1101 1010 0001 1010 to decimal 2c. Do the results of#2a and #2b have the same decimal value? Why or why not? 3a. Convert 8-bit two's complement 1001 0110 to decimal 3b. Convert 16-bit two's complement 0000 0000 1001 0110 to decimal 3c. Do the results of#3a and #3b have the same decimal value? Why or why not? 4a. Convert decimal 510 to 16-bit unsigned binary 4b. Convert decimal 510 to 16-bit two's complement binary 4c. Do the results of#4a and #4b have the same bit string? Why or why not? 5a. Convert decimal -510 to 16-bit two's complement bnary 5b. Treat the result ofthe previous problem as an unsigned 16-bit bimary number. Convert it to decimal 5c. Take the answer to 5b and add 510 to it. What do you get? Express the answer as a power of2 5d. Why do you get that power of2?

Explanation / Answer

1a)
Given unsigned binary: 0101 1010 0001 1010
By converting to decimal:

=>0(2^15)+1(2^14)+0(2^13)+1(2^12)+1(2^11)+0(2^10)+1(2^9)+0 (2^8)+0(2^7)+0(2^6)+0(2^5)+1(2^4)+ 1(2^3)+0(2^2)+1(2^1)+0(2^0) =>decimal = 23066

1b)
Given 2's complement is: 0101 1010 0001 1010
Given Number is poditive, since it starts with a '0'.
Flip the bits: 1010 0101 1110 0101
Add 1 to that 1's complement: 1010 0101 1110 0101
1
.....................
1010 0101 1110 0110 - -23066 signed decimal or 42470 decimal

1c)Both are not same they are differin their signs.

2a)
Given unsigned binary: 1101 1010 0001 1010
By converting to decimal:

=>1(2^15)+1(2^14)+0(2^13)+1(2^12)+1(2^11)+0(2^10)+1(2^9)+0 (2^8)+0(2^7)+0(2^6)+0(2^5)+1(2^4)+ 1(2^3)+0(2^2)+1(2^1)+0(2^0) =>decimal = 55834

2b)
Given 2's complement is: 1101 1010 0001 1010
Given Number is negative, since it starts with a '1'.
Flip the bits: 0010 0101 1110 0101
Add 1 to that 1's complement: 0010 0101 1110 0101
1
.....................
0010 0101 1110 0110 = 9702 decimal

2c)Both are not same.

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