1.
a)
[tex]111_2=1*2^0+1*2^1+1*2^2=1+2+4=7[/tex]
b)
[tex]10001_2=1*2^0+0*2^1+0*2^2+0*2^3+1*2^4=1+16=17[/tex]
c)
[tex]1101101_2=1*2^0+0*2^0+1*2^2+1*2^3+0*2^4+1*2^5+1*2^6=1+4+8+32+64=109[/tex]
2.
a)
[tex]2345:2=1172\ r\ 1\\1172:2=586\ r\ 0\\586:2=293\ r\ 0\\293:2=146\ r\ 1\\146:2=73\ r\ 0\\73:2=36\ r\ 1\\36:2=18\ r\ 0\\18:2=9\ r\ 0\\9:2=4\ r\ 1\\4:2=2\ r\ 0\\2:2=1\ r\ 0\\1:2=0\ r\ 1\\2345=100100101001_2[/tex]
b)
[tex]1256:2=628\ r\ 0\\628:2=314\ r\ 0\\314:2=157\ r\ 0\\157:2=78\ r\ 1\\78:2=39\ r\ 0\\39:2=19\ r\ 1\\19:2=9\ r\ 1\\9:2=4\ r\ 1\\4:2=2\ r\ 0\\2:2=1\ r\ 0\\1:2=0\ r\ 1\\1256=10011101000_2[/tex]
c)
[tex]5367:2=2683\ r\ 1\\2683:2=1341\ r\ 1\\1341:2=670\ r\ 1\\670:2=335\ r\ 0\\335:2=167\ r\ 1\\167:2=83\ r\ 1\\83:2=41\ r\ 1\\41:2=20\ r\ 1\\20:2=10\ r\ 0\\10:2=5\ r\ 0\\5:2=2\ r\ 1\\2:2=1\ r\ 0\\1:2=0\ r\ 1\\5367=1010011110111_2[/tex]
