Assume 161 and 214 are signed 8bit decimal integers stored i

Assume 161 and 214 are signed 8-bit decimal integers stored in two’s complement format. Calculate 161 – 214 using saturating arithmetic. The result should be written in decimal. Show your work

Solution

161

2|161 Remainders

2|80 1

2|40 0

2|20 0

2|10 0

2|5 0

2|2 1

2|1 0

|0 1

taking remainders in reverse order

(161)₁₀ = (10100001)₂

214

2|214 Remainders

2|107 0

2|53 1

2|26 1

2|13 0

2|6 1

2|3 0

2|1 1

|0 1

(214)₁₀ = (11010110)₂

-214 = 2\'s complement of 214

1s complement of 214 = 00101001

2\'s complement of 214 = +1

-214= 00101010

161-214 = 161 +(-214)

10100001

+ 00101010

= 11001011

now leftmost bit is 1 so the number is negative , so convert it into 2\'s complement

11001011

00110100 1s complement

+1 2\'s complement

( 00110101)₂ =(53)₁₀ and sign is negative

so result = -53

161-214 =-53