Question

How many binary digits are required to count 10010

Answer 1

Binary digits are required to count 10010:

Explanation:

• 64 32 16 8 4 2 1 numbering system can applied upto max. 127. i.e., 7 Binary Input.  
• Here 100 number is given and it is covered by 7 Binary digit as Input.
• Therefore, 7 is the correct answer (required binary digits to count).

Answer 2

7  binary digits are required to count 100₁₀

Given:

100₁₀

To Find:

Binary digits are required to count 100₁₀  ( Correct Question)

100 is in decimal system

Solution:

Decimal system use digits from 0 to 9  has base 10 as 10 digits are used

Binary system use digit 0 and 1  has base 2 as 2 digits are used

n Digits in binary can represent decimal from 0 to 2ⁿ - 1

Step 1:

Assume that n Binary digits are required to count 100₁₀ hence

2ⁿ - 1 ≥ 100

=> 2ⁿ ≥ 101

n = 6  => 2⁶ = 64 < 101

n = 7 => 2⁷ > 101

Hence n = 7 is the correct answer

7  binary digits are required to count 100₁₀

(Although you Question does not show 10 as base in Question but correct and complete Question is How many binary digits are required to count 100₁₀ )