Title: Number Systems: Negative Integers and Floating Point
1Department of Computer and Information
Science,School of Science, IUPUI
CSCI 230
Information Representation
Negative Integer Representation
Dale Roberts, Lecturer IUPUI droberts_at_cs.iupui.edu
2Negative Numbers in Binary
- Four different representation schemes are used
for negative numbers - Signed Magnitude
- Left most bit (LMB) is the sign bit
- 0 ? positive ()
- 1 ? negative (-)
- Remaining bits hold absolute magnitude
- Example
- 210 ? 0000 0010b
- -210 ? 1000 0010b
- Q 0000 0000 ?
- 1000 0000 ?
Try, 1000 0100b
-410
31s Complement
- Ones Complement
- Left most bit is the sign bit
- 0 ? positive ()
- 1 ? negative (-)
- The magnitude is Complemented
- Example
- 210 ? 0 000 0010b
- -210 ? 1 111 1101b
- Exercise try - 410 using 1s Complement
- Q 0000 0000 ?
- 1111 1111 ?
Solution 410 0 000 0100 b -410
111 1011 b
1
42s Complement
- 2s Complement
- Sign bit same as above
- Magnitude is Complemented first and a 1 is
added to the Complemented digits - Example
- 210 ? 0 000 0010b
- 1s Complement ? 1 111 1101b
- 1
- -210 ? 1 111 1110b
Exercise try -710 using 2s Complement
710 ? 1s Complement ? 1
-710 ?
0000 0111b
1111 1000b
1111 1001b
52s Complement
Example 7(-3) hint A B A (B) 1
- 710 0000 0111b
- 310 0000 0011b
- 1s complement 1111 1100b
- 2s complement 1111 1101b ? -310
- 7(-3) ? 0000 0111
- 1111 1101
-
-
1 1111 111 carry
ignore 1 0000 0100 ? 0000 0100 ? 410
6Three Representation of Signed Integer
7Negative Numbers in Binary (cont.)
- Excess Representation
- For a given fixed number of bits the range is
remapped such that roughly half the numbers are
negative and half are positive. - Example (as left)
- Excess 8 notation for 4 bit numbers
- Binary value 8 excess-8 value
- MSB can be used as a sign bit, but
- If MSB 1, positive number
- If MSB 0, negative number
- Excess Representation is also called bias
8Fundamental Data Types
- With vs. without using sign bit
- For a 16 bit binary pattern
9Fundamental Data Types
- Four Data Types in C (assume 2s complement, byte
machine)
Note 27 128, 215 32768, 215
2147483648 Complex and double complex are not
available
10Acknowledgements
- These slides where originally prepared by Dr.
Jeffrey Huang, updated by Dale Roberts.