Show the detailed steps involved in the following base conversions. Solve for X.
ID: 3744346 • Letter: S
Question
Show the detailed steps involved in the following base conversions. Solve for X. You must show your work.
2 10 b. 1151-X, c. 75426-X d. DEAD..-X e. 2457.-X 8 16 168Explanation / Answer
a) 101011111100 = 2^11 + 2^9 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 = 2048 + 512 + 128 + 64 + 32 + 16 + 8 + 4 = 2812 b) 115 (write it as powers of 2) = 64 + 32 + 16 + 2 + 1 = 11100110 c) 75426_8 first convert 75426 to binary octal binary 7 111 5 101 4 100 2 010 6 110 75426 => 0111 1011 0001 0110 binary hex 0111 7 1011 B 0001 1 0110 6 75246 in hexadecimal is 7B16 d) DEAD_(16) first convert DEAD to binary hex binary D 1101 E 1110 A 1010 D 1101 DEAD in binary is 001 101 111 010 101 101 binary octal 001 1 101 5 111 7 010 2 101 5 101 5 DEAD in octal is 157255 e) 2457_(8) = 2*8^3 + 4*8^2 + 5*8 + 7 = 2*512 + 4*64 + 40 + 7 = 1024 + 256 + 40 + 7 = 1327
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