ITPEC FE Morning April 2023 Question 2
When the hexadecimal value ABCD in a 32-bit register is logically shifted right by two bits, which of the following is the resulting value in hexadecimal?
Explanation
2AF3 — a logical right shift moves every bit two places right and fills the vacated top bits with 0.
- •
ABCDin binary (the upper 16 bits of the register are all 0):1010 1011 1100 1101 - •Shift right by 2: the low bits
01fall off and 0s enter at the top, giving0010 1010 1111 0011 - •Regroup into hexadecimal:
2AF3
Check: a logical right shift by 2 divides by 4 and drops the remainder. ABCD is 43981, 43981 ÷ 4 = 10995 remainder 1, and 10995 is 2AF3.
Answer (a)
Why not others:
- •(b) 6AF3 — a rotation right within 16 bits: the two bits
01that fell off are put back at the top - •(c) AF34 — a shift left by 2, with the result cut to 16 bits
- •(d) EAF3 — an arithmetic shift that copies the top bit of a 16-bit value; in a 32-bit register the top bit is 0, and a logical shift fills with 0 in any case
Key rule: A logical shift always fills with 0s, and the register width decides which bit is on top: a 32-bit register holding ABCD has 16 leading zeros.
Basic Theory · AI-written, may contain errors
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