Question

What are the decimal values of each of the following binary numbers if you interpret them as unsigned integers?

a)1111 1111 0000 0110
b)1111 1111 1110 1111
c)0111 1111 1110 1111
d)0101 0101 0101 0101

Answer 1

The binary numbers given are converted to the decimal system by calculating the sum of 2 raised to the power of each bit's position for the bits that are set to 1, starting from the right-most bit.

Step-by-step explanation:

The decimal values of each of the binary numbers interpreted as unsigned integers are calculated by summing the values of the '1' bits, where each bit represents a power of 2, depending on its position starting from the right (least significant bit).

1. 1111 1111 0000 0110 - This binary number is converted to decimal as follows: (1x2^15)+(1x2^14)+(1x2^13)+(1x2^12)+(1x2^11)+(1x2^10)+(1x2^9)+(1x2^8)+(0x2^7)+(0x2^6)+(0x2^5)+(0x2^4)+(0x2^3)+(1x2^2)+(1x2^1)+(0x2^0) = 65286.
2. 1111 1111 1110 1111 - In decimal, this is (1x2^15)+(1x2^14)+(1x2^13)+(1x2^12)+(1x2^11)+(1x2^10)+(1x2^9)+(1x2^8)+(1x2^7)+(1x2^6)+(1x2^5)+(0x2^4)+(1x2^3)+(1x2^2)+(1x2^1)+(1x2^0) = 65519.
3. 0111 1111 1110 1111 - The decimal equivalent is (0x2^15)+(1x2^14)+(1x2^13)+(1x2^12)+(1x2^11)+(1x2^10)+(1x2^9)+(1x2^8)+(1x2^7)+(1x2^6)+(1x2^5)+(0x2^4)+(1x2^3)+(1x2^2)+(1x2^1)+(1x2^0) = 32751.
4. 0101 0101 0101 0101 - This converts to (0x2^15)+(1x2^14)+(0x2^13)+(1x2^12)+(0x2^11)+(1x2^10)+(0x2^9)+(1x2^8)+(0x2^7)+(1x2^6)+(0x2^5)+(1x2^4)+(0x2^3)+(1x2^2)+(0x2^1)+(1x2^0) = 21845.