Integer Representations in Computer Memory

1. Different representationstostore integers Chapter 3

2. What is n ? n = number of bits allocated to represent the integer

3. Representations to store integers • Unsigned integer. • Sign-and-magnitude. • Two’s complement.

4. Unsigned integer representation • Range 0  2n -1 • STEPS:to store decimal integer in an n-bits memory location using unsigned integer representation. - covert (……..)10  (……)2- if number of bits < n  add 0s to the left. • STEPS: to retrieve a binary number stored in memory as an unsigned integer. covert (……..)2  (……)10 • Overflow:occurs if the decimal is out of range. ( occurs if binary bits > n )

5. Sign-and-magnitude representation • Range -( 2n-1 -1 )  +( 2n-1 -1 ) The leftmost bit defines the sign of the integer 0(+) , 1(-) • STEPS:to store decimal integer in an n-bits memory location using sign-and-magnitude representation . - store the sign in the leftmost bit.- covert (……..)10  (……)2 - use the remaining (n-1) bits to store the binary number. • STEPS: to retrieve a binary number stored in memory using sign-and-magnitude representation. - specify the sign from the leftmost bit.- the rest (n-1) bits is converted (……..)2  (……)10 • Overflow:occurs if the decimal is out of range.

6. Two’s complement representation • Range -( 2n-1)  +( 2n-1 -1 ) The leftmost bit defines the sign of the integer 0(+) , 1(-) • STEPS:to store decimal integer in an n-bits memory location using two’s complement representation.- the integer is changed to n bit binary( covert (……..)10  (……)2 ).- if the decimal integer is 0 or +  the binaryis stored as it is. is -  take the two’s complement. • STEPS: to retrieve a binary number stored in memory in two’s complement representation.- if Leftmost = 1  apply the two’s complement. Leftmost = 0  no operation is applied.- convert (……..)2  (……)10 - add the sign. • Overflow:occurs if the decimal is out of range.