Question

Express (118)10 and (-49)10 in 8-bit binary one’s complement form and then add the numbers. What would be the representation (-0)10 in 16-bit binary one’s complement? (be sure to show your work).

Answer 1

`118_(10)= 0110111` 2)
`-49_(10)=110001_(2)` 3)
`0_(10)=0:16 \Rightarrow 0_(10)=0_(16)`

Step-by-step explanation:

1) Expressing the Division as the summation of the quotient and the remainder

for

118, knowing it is originally a decimal form:

118:2=59 +(0), 59/2 =29 + 1, 29/2=14+1, 14/2=7+0, 7/2=3+1, 3/2=1+1, 1/2=0+1

`118_(10)= 0110111`

2)
`-49_(10)`

Similarly, we'll start the process with the absolute value of -49 since we want the positive value of it. Then let's start the successive divisions till zero.

|-49|=49

49:2=24+1, 24:2=12+0,12:2=6+0,6:2=3+0,3:2=1+1,1:2=0+1

100011

`-49_(10)=110001_(2)`

3)
`(-0)_(10)`

The first step on that is dividing by 16, and then dividing their quotient again by 16, so on and adding their remainders. Simply put:

`(-0)_(10)=0:16=0 \Rightarrow (0)_(10)=0_(16) \:or\\(0)_(16)=0000000000000000`