Question

II. Convert the following binary numbers into decimal numbers. Write the complete
steps.
(a) 1010010 (b) 1111100
by steps ​

Answer 1

Solution to a:

Given Binary Number,

= (1010 010)₂

We have to find out the decimal equivalent of the given number,

So, decimal equivalent will be,

= (1 × 2⁶) + (0 × 2⁵) + (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰)

= 64 + 0 + 16 + 0 + 0 + 2 + 0

= (82)₁₀ ★

Answer:

• (1010 010)₂ = (82)₁₀

Solution to b:

Given Binary Number,

= (1111 100)₂

Decimal equivalent will be,

= (1 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰)

= 64 + 32 + 16 + 8 + 4 + 0 + 0

= (124)₁₀ ★

Answer:

• (1111 100)₂ = (124)₁₀

Steps To Convert:

• Multiply each binary digit from right to left with the successive powers of 2 and add them up.
• Result obtained is the decimal equivalent of the number.

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