Question

E. Solve.
2. Convert 110001, to decimal form.​

Answer 1

Solution :

Here we have to convert 110001 from binary form to decimal form.

Number : 110001

Original Base : 2

Base to be converted in : 10

For converting from binary to decimal or in general any base to decimal , let us assume a case for any number abcdef and the original base being x .

To convert to decimal , you need to first multiply each digit of the number with the corresponding power of x starting from the rightmost digit(units digit) and the zeroth power

(abcdef)_x = [ ax⁵ + bx⁴ + cx³ + dx² + ex + f]_10

Doing the same here

(110001)_2 = [ 2⁵ + 2⁴ + 0 + 0 + 0 + 1] = 32 + 16 + 1 = 49.

(110001)_2 = (49)_10

This is the required answer .

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Answer 2

$\textsf{\large{\underline{Answer}:}}$

• The decimal equivalent of the given binary number (1100 01)₂ is (49)₁₀

$\textsf{\large{\underline{Solution}:}}$

Given Binary Number: (1100 01)₂

The Decimal Equivalent of the number will be:

= (1 × 2⁵) + (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰)

= 32 + 16 + 0 + 0 + 0 + 1

= (49)₁₀ (Answer)

$\textsf{\large{\underline{Steps To Solve}:}}$

• Multiply each binary digit starting from right with the successive powers of 2 (starting with 0).
• Add the products obtained after multiplication.
• Result obtained will be the decimal equivalent of the given binary number