Question

1. IN hex: a. Convert 1000 to hex; b. Add DEF to CBA.

Answer 1

Answer:

a) $(1000)_2=(8)_{10}$

b) DEF+ CBA =1AA9      

Step-by-step explanation:

To find : a) Convert 1000 to hex

b) Add DEF to CBA.

Solution :

a) Convert 1000 to hex

First we convert base 2 into base 10,

i.e. $(1000)_2=(1\times 2^3+0\times 2^2+0\times 2^1+0\times 2^0)_{10}$

$(1000)_2=(8+0+0+0)_{10}$

$(1000)_2=(8)_{10}$

Since, the digit 8 is same in both decimal and hexadecimal.

So, $(1000)_2=(8)_{10}$

b) Add DEF to CBA.

According to binary system,

A=10 , B=11 , C=12, D=13, E=14, F=15

Adding them with the following steps,

F=15 and A=10

So, 15+10=25

25 in hexadecimal is 19.

We put 9 at first place and forward 1 as a carry.

F=14 and B=11

So, 1+E+B=1+14+11=26

26 in hexadecimal is 1A.

We put A at second place and forward 1 as a carry.

D=13 and C=12

So, 1+D+C=1+13+12=26

26 in hexadecimal is 1A.

We put A at third place and forward 1 as a carry.

 D E F

+C B A

-------------

1 A A 9

Therefore, DEF+ CBA =1AA9