Question

Convert each following Base-R NUMBER TO THE equivalent BASE-10 NUMBER:

A);(AC)16

Convert each following base-10 number to equivalent number base 2,3,4,8,16

b):(175)10

c);(56.4)10

Answer 1

A) (AC)₁₆ = (172)₁₀

_Steps:

_{1.As 10 can be represented as A and 12 can be represented as C, this becomes 10 12}

_{2. 10*16¹ + 12* 16⁰ = 172}

b) To convert numbers from base 10 to base 2, following steps must be followed:

Step 1 : Divide the number by the value of the new base

Step 2 : Get the remainder from Step 2 as the least significant digit of new base number.

Step 3 : Divide the quotient of the previous divide by the new base.

Step 4: Store the remainder from Step 3 as the next digit of the new base number.

Repeat steps 3 and 4 till the quotient becomes 0. The remainder should be placed from right to left

Solving the following questions using this method we get:.

(175)₁₀ = (10101111)₂

(175)₁₀ = (20111)3

(175)₁₀ = (2233)4

(175)₁₀ = (257)8

(175)₁₀ = (af)16

c) Similarly,

(56.4)₁₀ = (1000110100)₂

(56.4)₁₀ = (202220)3

(56.4)₁₀ = (20310)4

(56.4)₁₀ = (1064)8

(56.4)₁₀ = (234)16