Signed versus Unsigned Integers

Question

Am I correct to say the difference between a signed and unsigned integer is   Unsigned can hold a larger positive value and no negative value  Unsigned uses the leading bit as a part of the value  while the signed version uses the left-most-bit to identify if the number is positive or negative  Signed integers can hold both positive and negative numbers   Any other differences

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According to what we learned in class  signed integers can represent both positive and negative numbers  while unsigned integers are only non-negative   For example  looking at an 8-bit number   unsigned values 0 to 255   signed values range from -128 to 127

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Unsigned integers are far more likely to catch you in a particular trap than are signed integers   The trap comes from the fact that while 1  amp  3 above are correct  both types of integers can be assigned a value outside the bounds of what it can  hold  and it will be silently converted   unsigned int ui   -1  signed int si   -1   if  ui  lt  0        printf  unsigned  lt  0 n      if  si  lt  0        printf  signed  lt  0 n      if  ui    si        printf   d     d n   ui  si       printf   ud     ud n   ui  si       When you run this  you ll get the following output even though both values were assigned to -1 and were declared differently   signed  lt  0 -1    -1 4294967295d    4294967295d

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Over and above what others have said  in C  you cannot overflow an unsigned integer  the behaviour is defined to be modulus arithmetic   You can overflow a signed integer and  in theory  though not in practice on current mainstream systems   the overflow could trigger a fault  perhaps similar to a divide by zero fault

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Generally speaking that is correct  Without knowing anything more about why you are looking for the differences I can t think of any other differentiators between signed and unsigned

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You must used unsigned Integers when programming on Embedded Systems  In loops  when there is no need for signed integers  using unsigned integers will save safe necessary for designing such systems

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Signed integers in C represent numbers   If a and b are variables of signed integer types  the standard will never require that a compiler make the expression a  b store into a anything other than the arithmetic sum of their respective values   To be sure  if the arithmetic sum would not fit into a  the processor might not be able to put it there  but the standard would not require the compiler to truncate or wrap the value  or do anything else for that matter if values that exceed the limits for their types   Note that while the standard does not require it  C implementations are allowed to trap arithmetic overflows with signed values   Unsigned integers in C behave as abstract algebraic rings of integers which are congruent modulo some power of two  except in scenarios involving conversions to  or operations with  larger types   Converting an integer of any size to a 32-bit unsigned type will yield the member corresponding to things which are congruent to that integer mod 4 294 967 296   The reason subtracting 3 from 2 yields 4 294 967 295 is that adding something congruent to 3 to something congruent to 4 294 967 295 will yield something congruent to 2   Abstract algebraic rings types are often handy things to have  unfortunately  C uses signedness as the deciding factor for whether a type should behave as a ring   Worse  unsigned values are treated as numbers rather than ring members when converted to larger types  and unsigned values smaller than int get converted to numbers when any arithmetic is performed upon them   If v is a uint32 t which equals 4 294 967 294  then v  v  should make v 4   Unfortunately  if int is 64 bits  then there s no telling what v  v  could do   Given the standard as it is  I would suggest using unsigned types in situations where one wants the behavior associated with algebraic rings  and signed types when one wants to represent numbers   It s unfortunate that C drew the distinctions the way it did  but they are what they are

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You must used unsigned Integers when programming on Embedded Systems  In loops  when there is no need for signed integers  using unsigned integers will save safe necessary for designing such systems

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Yes  unsigned integer can store large value  No  there are different ways to show positive and negative values  Yes  signed integer can contain both positive and negative values

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Everything except for point 2 is correct  There are many different notations for signed ints  some implementations use the first  others use the last and yet others use something completely different  That all depends on the platform you re working with

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I ll go into differences at the hardware level  on x86  This is mostly irrelevant unless you re writing a compiler or using assembly language  But it s nice to know   Firstly  x86 has native support for the two s complement representation of signed numbers  You can use other representations but this would require more instructions and generally be a waste of processor time   What do I mean by  native support   Basically I mean that there are a set of instructions you use for unsigned numbers and another set that you use for signed numbers  Unsigned numbers can sit in the same registers as signed numbers  and indeed you can mix signed and unsigned instructions without worrying the processor  It s up to the compiler  or assembly programmer  to keep track of whether a number is signed or not  and use the appropriate instructions   Firstly  two s complement numbers have the property that addition and subtraction is just the same as for unsigned numbers  It makes no difference whether the numbers are positive or negative   So you just go ahead and ADD and SUB your numbers without a worry    The differences start to show when it comes to comparisons  x86 has a simple way of differentiating them  above below indicates an unsigned comparison and greater less than indicates a signed comparison   E g  JAE means  Jump if above or equal  and is unsigned    There are also two sets of multiplication and division instructions to deal with signed and unsigned integers   Lastly  if you want to check for  say  overflow  you would do it differently for signed and for unsigned numbers

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I ll go into differences at the hardware level  on x86  This is mostly irrelevant unless you re writing a compiler or using assembly language  But it s nice to know   Firstly  x86 has native support for the two s complement representation of signed numbers  You can use other representations but this would require more instructions and generally be a waste of processor time   What do I mean by  native support   Basically I mean that there are a set of instructions you use for unsigned numbers and another set that you use for signed numbers  Unsigned numbers can sit in the same registers as signed numbers  and indeed you can mix signed and unsigned instructions without worrying the processor  It s up to the compiler  or assembly programmer  to keep track of whether a number is signed or not  and use the appropriate instructions   Firstly  two s complement numbers have the property that addition and subtraction is just the same as for unsigned numbers  It makes no difference whether the numbers are positive or negative   So you just go ahead and ADD and SUB your numbers without a worry    The differences start to show when it comes to comparisons  x86 has a simple way of differentiating them  above below indicates an unsigned comparison and greater less than indicates a signed comparison   E g  JAE means  Jump if above or equal  and is unsigned    There are also two sets of multiplication and division instructions to deal with signed and unsigned integers   Lastly  if you want to check for  say  overflow  you would do it differently for signed and for unsigned numbers

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Over and above what others have said  in C  you cannot overflow an unsigned integer  the behaviour is defined to be modulus arithmetic   You can overflow a signed integer and  in theory  though not in practice on current mainstream systems   the overflow could trigger a fault  perhaps similar to a divide by zero fault

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Everything except for point 2 is correct  There are many different notations for signed ints  some implementations use the first  others use the last and yet others use something completely different  That all depends on the platform you re working with

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Over and above what others have said  in C  you cannot overflow an unsigned integer  the behaviour is defined to be modulus arithmetic   You can overflow a signed integer and  in theory  though not in practice on current mainstream systems   the overflow could trigger a fault  perhaps similar to a divide by zero fault

User · Answer

Over and above what others have said  in C  you cannot overflow an unsigned integer  the behaviour is defined to be modulus arithmetic   You can overflow a signed integer and  in theory  though not in practice on current mainstream systems   the overflow could trigger a fault  perhaps similar to a divide by zero fault

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in answer to the second question  By only using a sign bit  and not 2 s complement   you can end up with -0  Not very pretty

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He only asked about signed and unsigned  Don t know why people are adding extra stuff in this  Let me tell you the answer    Unsigned  It consists of only non-negative values i e 0 to 255  Signed  It consist of both negative and positive values but in different formats like   0 to  127 -1 to -128    And this explanation is about the 8-bit number system

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Unsigned can hold a larger positive value and no negative value   Yes   Unsigned uses the leading bit as a part of the value  while the signed version uses the left-most-bit to identify if the number is positive or negative   There are different ways of representing signed integers   The easiest to visualise is to use the leftmost bit as a flag  sign and magnitude   but more common is two s complement   Both are in use in most modern microprocessors     floating point uses sign and magnitude  while integer arithmetic uses two s complement   Signed integers can hold both positive and negative numbers   Yes

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Another difference is when you are converting between integers of different sizes   For example  if you are extracting an integer from a byte stream  say 16 bits for simplicity   with unsigned values  you could do   i     int  b j    lt  lt  8   b j 1     should probably cast the 2nd byte  but I m guessing the compiler will do the right thing   With signed values you would have to worry about sign extension and do   i      int  b i    amp  0xFF   lt  lt  8     int  b i 1    amp  0xFF

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Generally speaking that is correct  Without knowing anything more about why you are looking for the differences I can t think of any other differentiators between signed and unsigned

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Another difference is when you are converting between integers of different sizes   For example  if you are extracting an integer from a byte stream  say 16 bits for simplicity   with unsigned values  you could do   i     int  b j    lt  lt  8   b j 1     should probably cast the 2nd byte  but I m guessing the compiler will do the right thing   With signed values you would have to worry about sign extension and do   i      int  b i    amp  0xFF   lt  lt  8     int  b i 1    amp  0xFF

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Everything except for point 2 is correct  There are many different notations for signed ints  some implementations use the first  others use the last and yet others use something completely different  That all depends on the platform you re working with

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He only asked about signed and unsigned  Don t know why people are adding extra stuff in this  Let me tell you the answer    Unsigned  It consists of only non-negative values i e 0 to 255  Signed  It consist of both negative and positive values but in different formats like   0 to  127 -1 to -128    And this explanation is about the 8-bit number system

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I ll go into differences at the hardware level  on x86  This is mostly irrelevant unless you re writing a compiler or using assembly language  But it s nice to know   Firstly  x86 has native support for the two s complement representation of signed numbers  You can use other representations but this would require more instructions and generally be a waste of processor time   What do I mean by  native support   Basically I mean that there are a set of instructions you use for unsigned numbers and another set that you use for signed numbers  Unsigned numbers can sit in the same registers as signed numbers  and indeed you can mix signed and unsigned instructions without worrying the processor  It s up to the compiler  or assembly programmer  to keep track of whether a number is signed or not  and use the appropriate instructions   Firstly  two s complement numbers have the property that addition and subtraction is just the same as for unsigned numbers  It makes no difference whether the numbers are positive or negative   So you just go ahead and ADD and SUB your numbers without a worry    The differences start to show when it comes to comparisons  x86 has a simple way of differentiating them  above below indicates an unsigned comparison and greater less than indicates a signed comparison   E g  JAE means  Jump if above or equal  and is unsigned    There are also two sets of multiplication and division instructions to deal with signed and unsigned integers   Lastly  if you want to check for  say  overflow  you would do it differently for signed and for unsigned numbers

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in answer to the second question  By only using a sign bit  and not 2 s complement   you can end up with -0  Not very pretty

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Generally speaking that is correct  Without knowing anything more about why you are looking for the differences I can t think of any other differentiators between signed and unsigned

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According to what we learned in class  signed integers can represent both positive and negative numbers  while unsigned integers are only non-negative   For example  looking at an 8-bit number   unsigned values 0 to 255   signed values range from -128 to 127

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The only guaranteed difference between a signed and an unsigned value in C is that the signed value can be negative  0 or positive  while an unsigned can only be 0 or positive  The problem is that C doesn t define the format of types  so you don t know that your integers are in two s complement   Strictly speaking the first two points you mentioned are incorrect

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in answer to the second question  By only using a sign bit  and not 2 s complement   you can end up with -0  Not very pretty

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Yes  unsigned integer can store large value  No  there are different ways to show positive and negative values  Yes  signed integer can contain both positive and negative values

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Unsigned can hold a larger positive value and no negative value   Yes   Unsigned uses the leading bit as a part of the value  while the signed version uses the left-most-bit to identify if the number is positive or negative   There are different ways of representing signed integers   The easiest to visualise is to use the leftmost bit as a flag  sign and magnitude   but more common is two s complement   Both are in use in most modern microprocessors     floating point uses sign and magnitude  while integer arithmetic uses two s complement   Signed integers can hold both positive and negative numbers   Yes

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Just a few points for completeness    this answer is discussing only integer representations   There may be other answers for floating point  the representation of a negative number can vary   The most common  by far - it s nearly universal today  in use today is two s complement   Other representations include one s complement  quite rare  and signed magnitude  vanishingly rare - probably only used on museum pieces  which is simply using the high bit as a sign indicator with the remain bits representing the absolute value of the number  When using two s complement  the variable can represent a larger range  by one  of negative numbers than positive numbers   This is because zero is included in the  positive  numbers  since the sign bit is not set for zero   but not the negative numbers  This means that the absolute value of the smallest negative number cannot be represented  when using one s complement or signed magnitude you can have zero represented as either a positive or negative number  which is one of a couple of reasons these representations aren t typically used

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in answer to the second question  By only using a sign bit  and not 2 s complement   you can end up with -0  Not very pretty

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Unsigned can hold a larger positive value and no negative value   Yes   Unsigned uses the leading bit as a part of the value  while the signed version uses the left-most-bit to identify if the number is positive or negative   There are different ways of representing signed integers   The easiest to visualise is to use the leftmost bit as a flag  sign and magnitude   but more common is two s complement   Both are in use in most modern microprocessors     floating point uses sign and magnitude  while integer arithmetic uses two s complement   Signed integers can hold both positive and negative numbers   Yes

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Everything except for point 2 is correct  There are many different notations for signed ints  some implementations use the first  others use the last and yet others use something completely different  That all depends on the platform you re working with

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I ll go into differences at the hardware level  on x86  This is mostly irrelevant unless you re writing a compiler or using assembly language  But it s nice to know   Firstly  x86 has native support for the two s complement representation of signed numbers  You can use other representations but this would require more instructions and generally be a waste of processor time   What do I mean by  native support   Basically I mean that there are a set of instructions you use for unsigned numbers and another set that you use for signed numbers  Unsigned numbers can sit in the same registers as signed numbers  and indeed you can mix signed and unsigned instructions without worrying the processor  It s up to the compiler  or assembly programmer  to keep track of whether a number is signed or not  and use the appropriate instructions   Firstly  two s complement numbers have the property that addition and subtraction is just the same as for unsigned numbers  It makes no difference whether the numbers are positive or negative   So you just go ahead and ADD and SUB your numbers without a worry    The differences start to show when it comes to comparisons  x86 has a simple way of differentiating them  above below indicates an unsigned comparison and greater less than indicates a signed comparison   E g  JAE means  Jump if above or equal  and is unsigned    There are also two sets of multiplication and division instructions to deal with signed and unsigned integers   Lastly  if you want to check for  say  overflow  you would do it differently for signed and for unsigned numbers

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The only guaranteed difference between a signed and an unsigned value in C is that the signed value can be negative  0 or positive  while an unsigned can only be 0 or positive  The problem is that C doesn t define the format of types  so you don t know that your integers are in two s complement   Strictly speaking the first two points you mentioned are incorrect

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Unsigned integers are far more likely to catch you in a particular trap than are signed integers   The trap comes from the fact that while 1  amp  3 above are correct  both types of integers can be assigned a value outside the bounds of what it can  hold  and it will be silently converted   unsigned int ui   -1  signed int si   -1   if  ui  lt  0        printf  unsigned  lt  0 n      if  si  lt  0        printf  signed  lt  0 n      if  ui    si        printf   d     d n   ui  si       printf   ud     ud n   ui  si       When you run this  you ll get the following output even though both values were assigned to -1 and were declared differently   signed  lt  0 -1    -1 4294967295d    4294967295d

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Just a few points for completeness    this answer is discussing only integer representations   There may be other answers for floating point  the representation of a negative number can vary   The most common  by far - it s nearly universal today  in use today is two s complement   Other representations include one s complement  quite rare  and signed magnitude  vanishingly rare - probably only used on museum pieces  which is simply using the high bit as a sign indicator with the remain bits representing the absolute value of the number  When using two s complement  the variable can represent a larger range  by one  of negative numbers than positive numbers   This is because zero is included in the  positive  numbers  since the sign bit is not set for zero   but not the negative numbers  This means that the absolute value of the smallest negative number cannot be represented  when using one s complement or signed magnitude you can have zero represented as either a positive or negative number  which is one of a couple of reasons these representations aren t typically used

User · Answer

Just a few points for completeness    this answer is discussing only integer representations   There may be other answers for floating point  the representation of a negative number can vary   The most common  by far - it s nearly universal today  in use today is two s complement   Other representations include one s complement  quite rare  and signed magnitude  vanishingly rare - probably only used on museum pieces  which is simply using the high bit as a sign indicator with the remain bits representing the absolute value of the number  When using two s complement  the variable can represent a larger range  by one  of negative numbers than positive numbers   This is because zero is included in the  positive  numbers  since the sign bit is not set for zero   but not the negative numbers  This means that the absolute value of the smallest negative number cannot be represented  when using one s complement or signed magnitude you can have zero represented as either a positive or negative number  which is one of a couple of reasons these representations aren t typically used

User · Answer

Just a few points for completeness    this answer is discussing only integer representations   There may be other answers for floating point  the representation of a negative number can vary   The most common  by far - it s nearly universal today  in use today is two s complement   Other representations include one s complement  quite rare  and signed magnitude  vanishingly rare - probably only used on museum pieces  which is simply using the high bit as a sign indicator with the remain bits representing the absolute value of the number  When using two s complement  the variable can represent a larger range  by one  of negative numbers than positive numbers   This is because zero is included in the  positive  numbers  since the sign bit is not set for zero   but not the negative numbers  This means that the absolute value of the smallest negative number cannot be represented  when using one s complement or signed magnitude you can have zero represented as either a positive or negative number  which is one of a couple of reasons these representations aren t typically used

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Generally speaking that is correct  Without knowing anything more about why you are looking for the differences I can t think of any other differentiators between signed and unsigned

User · Answer

Unsigned can hold a larger positive value and no negative value   Yes   Unsigned uses the leading bit as a part of the value  while the signed version uses the left-most-bit to identify if the number is positive or negative   There are different ways of representing signed integers   The easiest to visualise is to use the leftmost bit as a flag  sign and magnitude   but more common is two s complement   Both are in use in most modern microprocessors     floating point uses sign and magnitude  while integer arithmetic uses two s complement   Signed integers can hold both positive and negative numbers   Yes

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Signed integers in C represent numbers   If a and b are variables of signed integer types  the standard will never require that a compiler make the expression a  b store into a anything other than the arithmetic sum of their respective values   To be sure  if the arithmetic sum would not fit into a  the processor might not be able to put it there  but the standard would not require the compiler to truncate or wrap the value  or do anything else for that matter if values that exceed the limits for their types   Note that while the standard does not require it  C implementations are allowed to trap arithmetic overflows with signed values   Unsigned integers in C behave as abstract algebraic rings of integers which are congruent modulo some power of two  except in scenarios involving conversions to  or operations with  larger types   Converting an integer of any size to a 32-bit unsigned type will yield the member corresponding to things which are congruent to that integer mod 4 294 967 296   The reason subtracting 3 from 2 yields 4 294 967 295 is that adding something congruent to 3 to something congruent to 4 294 967 295 will yield something congruent to 2   Abstract algebraic rings types are often handy things to have  unfortunately  C uses signedness as the deciding factor for whether a type should behave as a ring   Worse  unsigned values are treated as numbers rather than ring members when converted to larger types  and unsigned values smaller than int get converted to numbers when any arithmetic is performed upon them   If v is a uint32 t which equals 4 294 967 294  then v  v  should make v 4   Unfortunately  if int is 64 bits  then there s no telling what v  v  could do   Given the standard as it is  I would suggest using unsigned types in situations where one wants the behavior associated with algebraic rings  and signed types when one wants to represent numbers   It s unfortunate that C drew the distinctions the way it did  but they are what they are

[integer] Signed versus Unsigned Integers

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