NUMBER BASE SYSTEM

PROBLEM 1

Write the decimal number 39 to base 2 (U.M.E 1980, Question 49)

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Problem 20

Add 1101₂, 10111₂ and 111₂

(A) 111011₂ (B) 110110₂ (C) 101011₂ (D) 101011₂ (E) 101010₂

(UME 2008, Question 1, Set U03)

Solution

 1101₂

10111₂

 +111₂

111011₂

 Answer: Option A

 

 

PROBLEM 21

If 125_x = 20₁₀. Find x (A) 2  (B) 3 (C) 4 (D) 5 (UME 2008, Question 2, Set U03)

Note: none of the options provided are correct

Reason:

for a base 2, its digits are 0,1

for a base 3, its digits are 0.1,2

for a base 4, its digits are 0,1,2,3

for a base 5, its digits are 0,1,2,3,4

 

 To prove this, let work it together

  

From our working x cannot be a negative integer so we ignore 5 and x cannot be 3, because for a base3 number, it digits that can occur are 0,1,2.

 

Problem 22

Subtract 16418₉ from 18630₉

(A) 1121₉ (B) 2112₉ (C)  2113₉ (D) 2211₉(UME 2009 Question 1, Set U03) 

 

Solution

18630₉

 16418₉

 2211₉

 

Problem 23

If 55_x + 52_x = 77₁₀, Find x(A) 5 (B)6 (C)  7 (D) 10 (UME 2009 Question 1, Set U03) 

Solution