Convert the octal number (347.24)_8 into its equivalent hexadecimal representation. Express as E7.5.
Octal (347.24)_8 to binary: 011 100 111 . 010 100. Group by 4 bits from radix point: 1110 0111 . 0101 0000 = (E7.5)_16.
In 8-bit 2's complement representation, what is the decimal equivalent of the binary string 11010110_2?
Since MSB is 1, it is negative. 2's complement of 11010110 is 00101010_2 = 42. So value is -42.
What is the range of integers that can be represented using 10-bit 2's complement form? Express as: minimum integer value.
For n-bit 2's complement, range is -$2^{n-1}$ to +$2^{n-1} - 1$. For $n=10$, -$2^9$ = -512.
Representing the decimal number +85 in 8-bit sign-magnitude, 1's complement, and 2's complement representations yields:
For positive numbers, sign-magnitude, 1's complement, and 2's complement representations are identical with MSB = 0.
In 4-bit 2's complement arithmetic, adding $A = 1001 (-7)$ and $B = 1010 (-6) results$ in an overflow. What is the decimal value of the resulting 4-bit sum without considering the carry-out?
1001 + 1010 = 10011. The 4-bit result is 0011 = +3 in decimal. Overflow occurs because two negative numbers yielded a positive result.