Shift Instructions [7M]

Shifts move bits left/right within register/word. Crucial for scaling (multiply/divide by $2^k$), bit manipulation, floating point normalization, I/O serialization.

Types:

1. Logical Shift:
Vacated bits filled with 0. Used for unsigned numbers.

• SHL / LSL Logical Shift Left: C <- b_{n-1} ... b0 <- 0 . E.g. 01010111 <<1 = 10101110, carry out =0. Equivalent to *2 (unsigned).
• SHR / LSR Logical Shift Right: 0 -> b_{n-1} ... b0 -> C. E.g. 10110011 >>2 = 00101100. Equivalent to unsigned /4.
  Example x86: SHL AX,1 , SHR BX, CL (CL = count).

2. Arithmetic Shift:
Preserves sign (for signed 2's complement).

• SAL = SHL (same for left).
• SAR Arithmetic Shift Right: vacated left bits filled with sign bit (MSB replicated). 1XXXX -> 11XXX. E.g. 11100100 (-28) SAR 1 = 11110010 (-14) correctly divides by 2. 01000000 (64) SAR1 =00100000 (32). LSR would give incorrect negative.

• Arithmetic left shift: sign bit not replicated; overflow checked via V flag if sign changes.

3. Circular / Rotate (no loss):
Bits that fall off are wrapped around.

• ROL Rotate Left: b_{n-1} -> b0 and -> Carry. ROR opposite. E.g. 10001111 ROL1 =00011111.
• RCL/RCR Rotate through Carry: Includes carry in loop (9-bit rotation for 8-bit reg). Used for multi-precision shifts: RCL propagates carry across words.
• Used for cryptography, bit extraction.

Hardware: Barrel shifter - combinational $n \times \log n$ mux network can shift any $k$ (0..n-1) in single cycle vs sequential shift register ($k$ cycles).

Applications & Examples:

• Multiplication/Division by power of 2: X *8 = SLL X,3 much faster than MUL. X/8 = SAR X,3 (signed).
• Example 8-bit: 00001101 (13) <<2 =00110100 (52)=13*4 .
• Multiplication of $14 *5$: 14 <<2 +14 = 56+14=70 without multiplier.
• Normalization: Floating addition requires align exponents via right shift of mantissa.
• Field extraction: MOV AL,mask; AND; SHR.

Flags: Shift updates C (last bit out), Z,S,P, arithmetic checks V/O.

Summary table:

Type	Fill	Use
LSL/SHL	0	Unsigned *$2^k$
LSR	0	Unsigned /$2^k$
ASR/SAR	sign	Signed /$2^k$
ROL/ROR	wrap	Rotate

Modern ISAs provide SHL, SHR, SAR, ROL, ROR, RCL, RCR, SHLD/SHRD (double precision shift).