x is a 16 bit register and x = 8395h. what is the result of the following operation in hexadecimal notation?
a: shr(x)
b: cil(X)
c: ashl(x)
d: dshr(x)
To calculate the results of the given operations, we need to understand the operations and their effects. Let's go through each operation one by one:
a) SHR (or logical shift right):
This operation performs a bitwise right shift on a binary number, which is equivalent to dividing the number by 2. In this case, we have a 16-bit register, x = 8395h. So, if we perform a SHR operation on x, we will shift all bits to the right by one position. The least significant bit will be lost, and a 0 will be brought in as the most significant bit (since the register is 16 bits). The result of SHR(x) is obtained by performing integer division by 2.
Calculating SHR(x):
x = 8395h = 1000 0011 1001 0101 in binary
SHR(x) = 1000 0011 1001 0101 >> 1 = 0100 0001 1100 1010 = 41CAh
b) CIL (or circular logical shift left):
This operation performs a bitwise rotation to the left on a binary number, where the bit that is shifted out from the most significant bit position is brought in at the least significant bit position. In other words, it rotates the bits to the left. The result of this operation is obtained by performing a bitwise OR with the shifted out bit.
Calculating CIL(x):
x = 8395h = 1000 0011 1001 0101 in binary
CIL(x) = (1000 0011 1001 0101 << 1) | (1000 0011 1001 0101 >> 15) = 0000 0111 0010 1010 | 0000 0000 0000 0001 = 072Bh
c) ASHL (or arithmetic shift left):
This operation is similar to the logical shift left, but it preserves the sign bit. If the most significant bit (sign bit) is 1, it will remain 1 after shifting. The result of the ASHL operation is obtained by performing an arithmetic shift left.
Calculating ASHL(x):
x = 8395h = 1000 0011 1001 0101 in binary
ASHL(x) = 1000 0011 1001 0101 << 1 = 0000 0111 0010 1010 = 072Ah
d) DSHR (or double shift right):
This operation performs a double bitwise right shift on a binary number. It is equivalent to performing two shr operations consecutively. The result of the DSHR operation is obtained by performing integer division by 4.
Calculating DSHR(x):
x = 8395h = 1000 0011 1001 0101 in binary
DSHR(x) = 1000 0011 1001 0101 >> 2 = 0010 0001 1100 1010 = 21CAh
So, the results of the given operations in hexadecimal notation are:
a) SHR(x) = 41CAh
b) CIL(x) = 072Bh
c) ASHL(x) = 072Ah
d) DSHR(x) = 21CAh