Number System Conversion addition subtraction Sample Question

Number System  Conversion addition subtraction Sample Question  For Quiz and assignment online Introduction to computing 

Q1.                                                                                                                                                                

a.       Convert (1110.01)₂ to base-10

1x2³ + 1x2² + 1x2¹ + 0x2⁰ + 0x2^-1 + 1x2^-2

 8+4+2+0+0+(1/4) = (14.25)₁₀

b.      Convert (10.101)₁₀ to base-2

Integer Part 10/2 = 5, 0 5/2 = 2, 1 2/2 = 1, 0 (10)10 = (1010)2

Factor 0.101 x 2 = 0.202 0.202 x 2 = 0.404 0.404 x 2 = 0.808 0.808 x 2 = 1.616

(10.101)₁₀ = (1010.0001)₂

c.       Convert (71.2)₈ to base-10

7x8¹ + 7x8⁰ + 7x8^-1

56 + 1 + 0.25 = 57.25

Q2.                                                                                                                                                                

a.       Perform the following addition

(AE9)₁₆ + (F)₁₆ = (AF8)₁₆ 

b.      Perform the following subtraction

(1111111)₂ – (111)₂ = (1111000)₂

c.       Perform the following addition

(231)₄ + (12)₄ = (303)₄