In: Computer Science
Convert 110.7510 to binary ______ and hexadecimal ______. Show the answer in both binary and hexadecimal.
There are ____________ kilobytes in a megabyte.
Convert -13210 to a 16-bit 2’s complement in binary ____________ and hexadecimal ______________.
Convert 110.75 to binary 1101110.11 and hexadecimal 0x6E.C. Show the answer in both binary and hexadecimal. There are 1024 kilobytes in a megabyte. Convert -132 to a 16-bit 2’s complement in binary 1111111101111100 and hexadecimal 0xFF7C. Explanation: ------------- 1) Converting 110.75 to binary Convert decimal part first, then the fractional part > First convert 110 to binary Divide 110 successively by 2 until the quotient is 0 > 110/2 = 55, remainder is 0 > 55/2 = 27, remainder is 1 > 27/2 = 13, remainder is 1 > 13/2 = 6, remainder is 1 > 6/2 = 3, remainder is 0 > 3/2 = 1, remainder is 1 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 1101110 So, 110 of decimal is 1101110 in binary > Now, Convert 0.75000000 to binary > Multiply 0.75000000 with 2. Since 1.50000000 is >= 1. then add 1 to result > Multiply 0.50000000 with 2. Since 1.00000000 is >= 1. then add 1 to result > This is equal to 1, so, stop calculating 0.75 of decimal is .11 in binary so, 110.75 in binary is 01101110.11 Hexadecimal Binary 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 A 1010 B 1011 C 1100 D 1101 E 1110 F 1111 Use this table to convert from binary to hexadecimal Converting 01101110.1100 to hexadecimal 0110 => 6 1110 => E 1100 => C So, in hexadecimal 01101110.1100 is 0x6E.C Answer: 0x6E.C 2) -132 This is negative. so, follow these steps to convert this into a 2's complement binary Step 1: Divide 132 successively by 2 until the quotient is 0 > 132/2 = 66, remainder is 0 > 66/2 = 33, remainder is 0 > 33/2 = 16, remainder is 1 > 16/2 = 8, remainder is 0 > 8/2 = 4, remainder is 0 > 4/2 = 2, remainder is 0 > 2/2 = 1, remainder is 0 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 10000100 So, 132 of decimal is 10000100 in binary So, 132 in normal binary is 0000000010000100 Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0. 0000000010000100 is flipped to 1111111101111011 Step 3:. Add 1 to above result 1111111101111011 + 1 = 1111111101111100 so, -132 in 2's complement binary is 1111111101111100 Converting 1111111101111100 to hexadecimal 1111 => F 1111 => F 0111 => 7 1100 => C So, in hexadecimal 1111111101111100 is 0xFF7C