# 1.1.2 Numbers in Bases Two, Eight and Five (Part 2)

(D) Converting Numbers in Base Two, Eight and Five to Base Ten and Vice Versa
1. Steps to convert numbers in base 2, 8 and 5 to base 10 are as follows.
(a) write the number in expanded notation.
(b) simplify the expanded notation into a single number.

Example 1:
Convert each of the following numbers to a number in base 10.
(a) 101012                     (b) 14238                     (c) 3245

Solution:
(a) 101012 = 1 × 24 + 0 × 23+ 1 × 22 + 0 × 21 + 1 × 20 = 2110
(b) 14238 = 1 × 83 + 4 × 82+ 2 × 81 + 3 × 80 = 78710
(c) 3245 = 3 × 52 + 2 × 51+ 4 × 50 = 8910

 Calculator Computation  1. Set the calculator to the ‘BASE’ mode by pressing:     [MODE]   [MODE]   [3 (BASE)] 2. Set the calculator to the desired number system by pressing: [BIN] → for base 2 [DEC] → for base 10 [OCT] → for base 8 Key in the following: (a) [BIN] 10101 [=]  [ DEC ] The screen display is: [21] Therefore 101012 = 2110 (b) [OCT] 1423 [=]  [ DEC ] The screen display is: [787] Therefore 14238 = 78710

2. Steps to convert a number in base 10 to a number in base 2, 8 and 5 are as follows.
(a) perform repeated division until the quotient is zero.
(b) write the number in new base by referring to the remainders from bottom to the top.

Example 2:
Convert 6110 to a number in
(a) Base two                    (b) base eight                  (c) base five

Solution:

(a)

(b)

(c)

 Calculator Computation 1. Set the calculator to the ‘BASE’ mode by pressing:     [MODE]   [MODE]   [3 (BASE)] 2. Set the calculator to the desired number system by pressing: [BIN] → for base 2 [DEC] → for base 10 [OCT] → for base 8 Key in the following: (a) [DEC] 61 [=]  [ BIN ] The screen display is: [1111012] Therefore 6110 = 1111012 (b) [DEC] 61 [=]  [ OCT ] The screen display is: [75] Therefore 6110 = 758