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Department of Computer and Information Science, School of Science, IUPUI. CSCI 230. Information Representation: Negative Integer Representation . Dale Roberts, Lecturer IUPUI droberts@cs.iupui.edu. Negative Numbers in Binary.

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Department of Computer and Information Science,School of Science, IUPUI

CSCI 230

Information Representation:

Negative Integer Representation

Dale Roberts, Lecturer

IUPUI

droberts@cs.iupui.edu

Negative 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

1’s Complement
• One’s 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 - 410using 1’s Complement

Q: 0000 0000 = ?

1111 1111 = ?

Solution:

410 = 0 0000100b

-410 =

1

1111011b

2’s Complement
• 2’s Complement
• Sign bit same as above
• Magnitude is Complemented first and a “1” is added to the Complemented digits
• Example:
• 210 0 000 0010b
• 1’s Complement  1 1111101b
• +1
• -210 1 111 1110b
• Exercise: try -710using 2’s Complement
• 710
• 1’s Complement 
• +1
• -710 

0000 0111b

11111000b

• 1111 1001b
2’s Complement

710 = 0000 0111b

310 = 0000 0011b

1’s complement 1111 1100b

2’s complement 1111 1101b -310

7+(-3)  0000 0111

+ 1111 1101

• Example: 7+(-3) [hint]: A – B = A + (~B) +1

1 1111 111 carry

• ignore 1 0000 0100  0000 0100 410
Negative 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
Fundamental Data Types
• With vs. without using sign bit
• For a 16 bit binary pattern:
Fundamental Data Types
• Four Data Typesin C(assume 2’s complement, byte machine)
• Note: 27 = 128, 215 =32768, 215 = 2147483648
• Complex and double complex are not available
Acknowledgements
• These slides where originally prepared by Dr. Jeffrey Huang, updated by Dale Roberts.