Chapter 3, Problem 2TQ

Explanation of Solution

Converting whole numbers from one base to another:

The number has to be divided by the new base while converting a whole number from one base to another.

Example:

• Consider the whole number ${\left(\text{3426}\right)}_{\text{10}}$ , to convert this number to base 16 , that number has to be divided by the new base “16”.
• The conversion process is as follows,

• In base 10, the value “3246” is represented in positional notation as,
  • $\text{3}\times {\text{10}}^3{\text{+4×10}}^{\text{2}}{\text{+2×10}}^{\text{1}}{\text{+6×10}}^{\text{0}}\text{=3426}$
    • The positional notation for base 10 value results in correct value

Explanation of Solution

Converting fractional parts from one base to another:

The number has to be multiplied by the new base while converting a fractional part from one base to another.

Example:

• Consider the fractional number ${\left(5.896\right)}_{\text{10}}$, to convert this number to base 16, that number has to be divided by the new base “16”.
• The conversion process is as follows,

• In base 10, the value “${\left(5.896\right)}_{\text{10}}$” is represented in positional notation as,
  • ${\text{5×10}}^{\text{0}}{\text{. 8×10}}^{-\text{1}}{\text{+9×10}}^{-\text{2}}{\text{+6×10}}^{-\text{3}}\text{=5}$