Question

4. Convert the following Binary numbers into its decimal equivalent.
A. 1001
B. 11001
C. 100100
D. 110011
pls tell all 4​

Answer 1

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

• (1001)₂ = (9)₁₀
• (1100 1)₂ = (25)₁₀
• (1001 00)₂ = (36)₁₀
• (1100 11)₂ = (51)₁₀

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

#1

Given Binary Number: (1001)₂

The Decimal Equivalent of the number will be:

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

= 8 + 0 + 0 + 1

= (9)₁₀ (Answer)

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#2

Given Binary Number: (1100 1)₂

The Decimal Equivalent of the number will be:

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

= 16 + 8 + 0 + 0 + 1

= (25)₁₀ (Answer)

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#3

Given Binary Number: (1001 00)₁₀

The Decimal Equivalent of the number will be:

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

= 32 + 0 + 0 + 4 + 0 + 0

= (36)₁₀ (Answer)

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#4

Given Binary Number: (1100 11)₂

The Decimal Equivalent of the number will be:

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

= 32 + 16 + 0 + 0 + 2 + 1

= (51)₁₀ (Answer)

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

• Multiply each binary digits 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 numbers.

Answer 2

Answer:

A = 9

B = 25

C = 36

D = 51

Explanation:

A = (1001)₂ = (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰) = (9)₁₀

B = (11001)₂ = (1 × 2⁴) + (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰) = (25)₁₀

C =  (100100)₂ = (1 × 2⁵) + (0 × 2⁴) + (0 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰) = (36)₁₀

D = (110011)₂ = (1 × 2⁵) + (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = (51)₁₀