Question

What is the decimal and hexadecimal equivalent of the largest binary that can be expressed with 12 digits?

Answer 1

Answer:

decimal equivalent = 4095

hexadecimal equivalent = FFF

Explanation:

the largest binary that can be expressed with 12 digits is 111111111111

For binary number with n digits:

d n-1 ... d 3 d 2 d 1 d 0

The decimal number is equal to the sum of binary digits (d n) times their power of 2 (2^n):

decimal = d₀×20 + d₁×21 + d₂×22 + ...

so 111111111111 = (1 × 2¹¹) + (1 × 2¹⁰) + (1 × 2⁹) + (1 × 2⁸) + (1 × 2⁷) + (1 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (1 × 2⁰) = 4095

decimal equivalent = 4095

we know that the hexadecimal equivalent for 1111 is F

so the hexadecimal equivalent for 111111111111 is FFF