HCMC University of Technical Education
Faculty of Electrical & Electronic Engineering
Lecture:
DIGITAL SYSTEMS
Chapter 5: Digital Arithmetic
Representing Signed Numbers
Assoc. Prof. Nguyen Thanh Hai, PhD
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HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
Representing Signed Numbers
Figure shows 2 registers which contain binary numbers, in which
cells from A0 to A5 contain bits 0/1 and cell A6 is for sign-bit,
particularly 0 (sign bit +) and 1 (sign bit -).
Representation of six-bit FF registers with
signed numbers in sign-magnitude form
Assoc. Prof. Nguyen Thanh Hai, PhD
2
HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
Representing Signed Numbers
1’s-Complement Form
101101
original binary number
Changing each 0 to 1 and each 1 to 0
010010
complement each bit to form 1’s complement
2’s-Complement Form
+
101101
binary equivalent of +4510
010010
Changing to form 1’s complement
000001
add 1 to form 2’s complement
010011
2’s complement (-4510) of original binary
number
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Assoc. Prof. Nguyen Thanh Hai, PhD
HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
Representing Signed Numbers
Example
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Assoc. Prof. Nguyen Thanh Hai, PhD
HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
Representing Signed Numbers
5
Assoc. Prof. Nguyen Thanh Hai, PhD
HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
Representing Signed Numbers
b. 11010
11010; bù 1: 00101; bù 2: 00110
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Assoc. Prof. Nguyen Thanh Hai, PhD
HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
Representing Signed Numbers
Outcome assessment questions
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Assoc. Prof. Nguyen Thanh Hai, PhD
HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
Representing Signed Numbers
The End
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Assoc. Prof. Nguyen Thanh Hai, PhD