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

Answer:a) [tex](1000)_2=(8)_{10}[/tex]b) DEF+ CBA =1AA9       Step-by-step explanation:To find : a) Convert 1000 to hexb) Add DEF to CBA.Solution : a) Convert 1000 to hexFirst we convert base 2 into base 10,i.e. [tex](1000)_2=(1\times 2^3+0\times 2^2+0\times 2^1+0\times 2^0)_{10}[/tex][tex](1000)_2=(8+0+0+0)_{10}[/tex][tex](1000)_2=(8)_{10}[/tex]Since, the digit 8 is same in both decimal and hexadecimal.So, [tex](1000)_2=(8)_{10}[/tex]b) Add DEF to CBA.According to binary system,A=10 , B=11 , C=12, D=13, E=14, F=15Adding them with the following steps,F=15 and A=10So, 15+10=2525 in hexadecimal is 19.We put 9 at first place and forward 1 as a carry.F=14 and B=11So, 1+E+B=1+14+11=2626 in hexadecimal is 1A.We put A at second place and forward 1 as a carry.D=13 and C=12So, 1+D+C=1+13+12=2626 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 9Therefore, DEF+ CBA =1AA9