Answer to Question #342587 in Discrete Mathematics for Dreaper

Question

Representation of intergers

Change the following number systems to base-10 numbers.

• 1101101001₂
• 5522₈
• 12CF₁₆

Answer 1

a.

$$(1101101001)_2=2^9+2^8+2^6+2^5+2^3+2^0$$

$$=512+256+64+32+8+1=873$$

b.

$$(5522)_8=5(8)^3+5(8)^2+2(8)^1+2(8)^0$$

$$=2560+320+16+2=2898$$

c.

$$(12CF)_{16}=1(16)^3+2(16)^2+12(16)^1+15(16)^0$$

$$=4096+512+192+15=4815$$