 # Left shift multiply by 2

Logical Shift and Arithmetic Shift are bit manipulation operations bitwise operations. The result of a Left Shift operation is a multiplication by 2 nwhere n is the number of shifted bit positions. By shifting in to the left with one position we get which is 4 in decimal representation. If we shift it once more we get binary value which is 8 in decimal representation. The result of the multiplication is larger than the largest possible.

Shifting left on signed values also works, but overflow occurs when the most significant bit changes values from 0 to 1, or 1 to 0. The result of a Right Shift operation is a division by 2 nwhere n is the number of shifted bit positions. If we have the binary number decimal and we perform arithmetic right shift by 1 bit we get the binary number 58 decimal.

So we have divided the original number by 2. If we have the binary number -6 decimal and we perform arithmetic right shift by 1 bit we get the binary number -3 decimal. So we have divided the original negative number by 2.

By shifting in to the right with one position we get which is 4 in decimal representation. I suggest you just say, By shifting left, we multiply. Hello brad, Thanks for catching the mistake and providing us with a feedback.

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We will fix the wording in the article. Hello skywood, By definition the left shift operation discards the MSB and this indeed may cause overflow which is undesired in almost every digital system. The solution is to implement additional logic functionality that saturates the result of the shift operation if an overflow has occurred.

This is all assuming signed magnitude representation, which worked for understanding all the preceding examples. Also, add the interpreted values into the final example to make it clearer that the result is correct. Hello Tama, Thank you for the feedback! We have updated the article and it now incorporates your suggestion.

Keep in mind that one additional left shift of this 8bit binary number will cause an overflow and you should take precautions :. This site uses Akismet to reduce spam. Learn how your comment data is processed. Home Digital Logic Logical Vs. Arithmetic Shift. Previous Next. A Right Logical Shift of one position moves each bit to the right by one.

Was this article helpful? If you have any suggestions or questions, please leave a comment below. Related Posts. Digital Buffers And Their Usage. May 20th, 1 Comment. Microprocessor Instruction Pipelining.In computer programmingan arithmetic shift is a shift operatorsometimes termed a signed shift though it is not restricted to signed operands.

The two basic types are the arithmetic left shift and the arithmetic right shift. For binary numbers it is a bitwise operation that shifts all of the bits of its operand; every bit in the operand is simply moved a given number of bit positions, and the vacant bit-positions are filled in. Instead of being filled with all 0s, as in logical shiftwhen shifting to the right, the leftmost bit usually the sign bit in signed integer representations is replicated to fill in all the vacant positions this is a kind of sign extension.

Some authors prefer the terms sticky right-shift and zero-fill right-shift for arithmetic and logical shifts respectively. Arithmetic shifts can be useful as efficient ways to perform multiplication or division of signed integers by powers of two.

Shifting left by n bits on a signed or unsigned binary number has the effect of multiplying it by 2 n.

## Left Shift and Right Shift Operators in C/C++

Shifting right by n bits on a two's complement signed binary number has the effect of dividing it by 2 nbut it always rounds down towards negative infinity. This is different from the way rounding is usually done in signed integer division which rounds towards 0.

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This discrepancy has led to bugs in more than one compiler. For example, in the x86 instruction setthe SAR instruction arithmetic right shift divides a signed number by a power of two, rounding towards negative infinity. The formal definition of an arithmetic shift, from Federal Standard C is that it is:.

Arithmetic left shifts are equivalent to multiplication by a positive, integral power of the radix e. Logical left shifts are also equivalent, except multiplication and arithmetic shifts may trigger arithmetic overflow whereas logical shifts do not. However, arithmetic right shifts are major traps for the unwary, specifically in treating rounding of negative integers.

This corresponds to rounding down towards negative infinitybut is not the usual convention for division. It is frequently stated that arithmetic right shifts are equivalent to division by a positive, integral power of the radix e. A shifter is much simpler than a divider. On most processors, shift instructions will execute faster than division instructions. Logical right shifts are equivalent to division by a power of the radix usually 2 only for positive or unsigned numbers.

Arithmetic right shifts are equivalent to logical right shifts for positive signed numbers. Arithmetic right shifts for negative numbers are equivalent to division using rounding towards 0 in one's complement representation of signed numbers as was used by some historic computers, but this is no longer in general use. The ISO standard for the programming language C defines the right shift operator in terms of divisions by powers of 2.

It does not specify the behaviour of the right shift operator in such circumstances, but instead requires each individual C compiler to define the behaviour of shifting negative values right. In applications where consistent rounding down is desired, arithmetic right shifts for signed values are useful. An example is in downscaling raster coordinates by a power of two, which maintains even spacing.

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Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. To multiply in terms of adding and shifting you want to decompose one of the numbers by powers of two, like so:.

As you can see, multiplication can be decomposed into adding and shifting and back again.

### Logical Vs. Arithmetic Shift

Real computer systems as opposed to theoretical computer systems have a finite number of bits, so multiplication takes a constant multiple of time compared to addition and shifting. If I recall correctly, modern processors, if pipelined properly, can do multiplication just about as fast as addition, by messing with the utilization of the ALUs arithmetic units in the processor.

The answer by Andrew Toulouse can be extended to division. The division by integer constants is considered in details in the book "Hacker's Delight" by Henry S.

Warren ISBN The first idea for implementing division is to write the inverse value of the denominator in base two.

One of the fastest ways to divide by integer constants is to exploit the modular arithmetics and Montgomery reduction: What's the fastest way to divide an integer by 3? To divide a number by a non-power of two, I'm not aware of any easy way, unless you want to implement some low-level logic, use other binary operations and use some form of iteration. I translated the Python code to C. The example given had a minor flaw. If the dividend value that took up all the 32 bits, the shift would fail. I just used bit variables internally to work around the problem:. Take one of the numbers, in this case, we'll call it A, and shift it right by one bit, if you shift out a one, add the first number, we'll call it B, to R.

A procedure for dividing integers that uses shifts and adds can be derived in straightforward fashion from decimal longhand division as taught in elementary school. The selection of each quotient digit is simplified, as the digit is either 0 and 1: if the current remainder is greater than or equal to the divisor, the least significant bit of the partial quotient is 1. Just as with decimal longhand division, the digits of the dividend are considered from most significant to least significant, one digit at a time.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Software Engineering Stack Exchange is a question and answer site for professionals, academics, and students working within the systems development life cycle. It only takes a minute to sign up. Just by looking at this there are several more instructions in the divide version compared to the bit shift. This additional work, knowing that we're dealing with a math rather than bits is often necessary to avoid various errors that can occur by doing just bit math.

Here the compiler was able to identify that the math could be done with a shift, however instead of a logical shift it does a arithmetic shift. The difference between these would be obvious if we ran these - sarl preserves the sign. Its right, but its not integer multiplication. And thus be wary of premature optimization. Let the compiler optimize for you - it knows what you're really trying to do and will likely do a better job of it, with fewer bugs. The existing answers didn't really address the hardware side of things, so here's a bit on that angle. The conventional wisdom is that multiplication and division are much slower than shifting, but the actual story today is more nuanced.

For example, it is certainly true that multiplication is a more complex operation to implement in hardware, but it doesn't necessarily always end up slower. As it turns out, add is also significantly more complex to implement than xor or in general any bitwise operationbut add and sub usually get enough transistors dedicated to their operation that end up being just as fast as the bitwise operators.

### Arithmetic shift

So you can't just look at hardware implementation complexity as a guide to speed. So let's look in detail at shifting versus the "full" operators like multiplication and shifting.

On nearly all hardware, shifting by a constant amount i. In particular, it will usually happen with a latency of a single cycle, and with a throughput of 1 per cycle or better. On some hardware e. Shifting by a variable amount is more of a grey area. On older hardware, this was sometimes very slow, and the speed changed from generation to generation. For example, on the initial release of Intel's P4, shifting by a variable amount was notoriously slow - requiring time proportional to the shift amount!

On that platform, using multiplications to replace shifts could be profitable i. On prior Intel chips, as well as subsequent generations, shifting by a variable amount wasn't so painful. On current Intel chips, shifting by a variable amount is not particularly fast, but it isn't terrible either.

The x86 architecture is hamstrung when it comes to variable shifts, because they defined the operation in an unusual way: shifts amounts of 0 don't modify the condition flags, but all other shifts do.

This inhibits the efficient renaming of the flags register since it can't be determined until the shift executes whether subsequent instructions should read the condition codes written by the shift, or some prior instruction.

Furthermore, shifts only write to part of the flags register, which may cause a partial flags stall. The upshot then is that on recent Intel architectures, shift by a variable amount takes three "micro-operations" while most other simple operations add, bitwise ops, even multiplication only take 1. Such shifts can execute at most once every 2 cycles. The trend in modern desktop and laptop hardware is to make multiplication a fast operation.

On recent Intel and AMD chips, in fact, one multiplication can be issued every cycle we call this reciprocal throughput. The latencyhowever, of a multiplication is 3 cycles. So that means you get the result of any given multiplication 3 cycles after you start it, but you are able to start a new multiplication every cycle. Which value 1 cycle or 3 cycles is more important depends on the structure of your algorithm. If the multiplication is part of a critical dependency chain, the latency is important.The type of the second operand must be an int.

For binary numbers it is a bitwise operation that shifts all of the bits of its operand; every bit in the operand is simply moved a given number of bit positions, and the vacant bit-positions are filled in. Arithmetic shifts can be useful as efficient ways of performing multiplication or division of signed integers by powers of two. Shifting left by n bits on a signed or unsigned binary number has the effect of multiplying it by 2 n. Shifting right by n bits on a two's complement signed binary number has the effect of dividing it by 2 nbut it always rounds down towards negative infinity.

This is different from the way rounding is usually done in signed integer division which rounds towards 0. This discrepancy has led to bugs in more than one compiler. An other usage is work with color bits.

However It is worth noting that depending on whether the operand is a signed integral type or a unsigned integral type it will apply either an arithmetic or logical shift.

See the bottom of this page on msdn. Follow this link for more detailed information. For example, if x was and y was 1 then the result would be It's like someone's pushed each bit left one. Usage Arithmetic shifts can be useful as efficient ways of performing multiplication or division of signed integers by powers of two.

Please give a quick explaination of this expression. As a few people have pointed out already it is a shift operation. It's called left-shift operator. Shift left and the counterpart, Shift right moves the bits in the given direction. Shift left is more or less times 2, but faster Shift right is more or less divided by 2, but faster.

What is the difference between String and string in C? Hidden Features of C? Does Python have a ternary conditional operator? What is the!! Reference — What does this symbol mean in PHP? What are the basic rules and idioms for operator overloading? What does the C??!??!Bitwise Operators 3. The Bitwise Operators can be applied to the integer types, long, int, short, char, and byte. The Bitwise Logical Operators 3. Bitwise OR 3. Left shift 3. Demonstrate the bitwise logical operators 3.

All bitwise operators in action 3. Bitwise Operator Assignments 3. The Left Shift 3. Left shifting as a quick way to multiply by 2 3. The Right Shift 3.

The Unsigned Right Shift 3. Signed shift to the right 3. Unsigned shifting a byte value. Convert a number to negative and back 3. Performing Bitwise Operations on a Bit Vector 3. Returns a byte array of at least length 1 3. Use bitwise operator to create hash code 3. Operations on bit-mapped fields. The Bitwise Logical Operators. Demonstrate the bitwise logical operators. All bitwise operators in action.

Bitwise Operator Assignments. The Unsigned Right Shift.By Joel YliluomaJanuary How to implement various arithmetic and logical operations on platforms without native support for those operations.

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Two's complement is assumed. Addition without carry Using subtraction Addition can be synthesized from subtraction by negating the source operand. Addition can be synthesized bit by bit using the logical XOR operation.

Alternatively, you can get carry by calculating with integer sizes larger than the source operands are. This produces a carry flag, too. If you don't have any OR or AND operations, but you do have a shift-to-right-with-carry or a rotate-to-right-with-carry, you can implement addition using those.

When you need to add together integers that are larger than your native register size, you need to utilize the carry. Using addition Subtraction can be synthesized from addition by negating the source operand. For platforms without sub-with-carry, carry can be synthesized by comparing the result to the original. Subtract the operand from an integer where every bit is 1.

Negate the operand and subtract one. Depends on two's complement arithmetic. If you have an operation that tests whether a particular bit is set, you can implement AND using a loop. Bit-wise OR, i. If you have an operation that tests whether a particular bit is set, you can implement OR using a loop.

You can test bit by bit whether the bit is different in both operands.

32. Multiplying by 2^n using Left shift operation (Adding zeroes to the right)

Logical bit-shifting to the left can be accomplished by multiplying the value by 2, i. It's often needed. Logical bit-shifting to the right can be accomplished by dividing the value by 2, assuming division always rounds towards zero. Without divisions Logical bit-shifting to the right can also be accomplished through logical bit-shifting to the LEFT by inverse the amount. This requires the use of a register that is double the original's size.