1. Speaker: Fuw-Yi Yang 楊伏夷 伏夷非征番, 道德經 察政章(Chapter 58) 伏者潛藏也
數位系統  Digital Systems 
Department of Computer Science and Information Engineering, Chaoyang University of Technology
朝陽科技大學資工系
Speaker: Fuw-Yi Yang 楊伏夷
伏夷非征番,
道德經 察政章(Chapter 58) 伏者潛藏也
道紀章(Chapter 14) 道無形象, 視之不可見者曰夷
Fuw-Yi Yang

2. Text Book: Digital Design 4th Ed. Chapter 1 Problems
1.19 The following decimal numbers are shown in sign-magnitude form: +9,286 and Convert them to sign-10’s-complement form and perform the following operations (note that the sum is +10,627 and requires five digits and a sign).
Definition and solution: next pages
Fuw-Yi Yang

3. Text Book: Digital Design 4th Ed. Chap 1 1.5 Complements
Diminished Radix Complement
Given a number N in base r having n digits, the (r - 1)’s
complement of N is defined as (rn - 1) - N.
N = 9286, r = 10, n = 5
The 9’s complement of N is ( ) = 90713
Radix Complement
Given a number N in base r having n digits, the r’s
complement of N is defined as
rn - N for N 0 and as 0 for N = 0 .
The 10’s complement of N is = 90714
Fuw-Yi Yang

4. Text Book: Digital Design 4th Ed. Chapter 1 Problems
Sol. 1-19
(+9286) + (+ 801) = =
Sign bit = 0 , answer = (+10087)
(b) (-9286) + (801) = (990714) + (000801) =
Sign bit = 1 , answer is a negative number
represented in 10’s-complement form (991515),
or= -( ) = -8485
009286
010087
Sign bit
990714
991515
Fuw-Yi Yang

5. Text Book: Digital Design 4th Ed. Chapter 1 Problems
Next page shows an implementation of adder-subtractor using 2’s complement form (1 sign bit and 3-bit magnitude).
No overflow can occur in the cases: (+ number) + (- number) and
(- number) + (+ number)
Overflow may occur in the cases: (+ number) + (+ number) and
(- number) + (- number)
(+5) + (+6) = (-5) + (-6) =
Carry in the sign bit position, Carry out of sign bit position
Fuw-Yi Yang

6. Text Book: Digital Design 4th Ed. Chap 4.5 Binary Adder-Subtractor
Sign bit position
Over flow occurs when either Carry in the sign bit position or Carry out of sign bit position but not both or none of them.
Fuw-Yi Yang