What is the greatest number that can be presented in four digits in the followin

Question

What is the greatest number that can be presented in four digits in the following number systems? Show your work:

a. Hexadecimal

b. Binary

c. Decimal

d. Octal

Convert a, b and d to decimal system.

Explanation / Answer

a. Hexadecimal Answer: FFFF In decimal it is => 15*16^3 + 15*16^2 + 15*16^1 + 15 => 61440 + 3840 + 240 + 15 => 65535 Answer in decimal: 65535 b. Binary Answer: 1111 In decimal it is => 1*2^3 + 1*2^2 + 1*2^1 + 1 => 8 + 4 + 2 + 1 => 15 Answer in decimal: 15 c. Decimal Answer: 9999 Answer in decimal: 9999 d. Octal Answer: 7777 In decimal it is => 7*8^3 + 7*8^2 + 7*8^1 + 7 => 3584 + 448 + 56 + 7 => 4095 Answer in decimal: 4095

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