Question Solved1 Answer 5. Show how each of the following signed, decimal integers would be stored in 8-bit two's complement code. Give your answer in hexadecimal. a. +100 b. -1 C. -10 d. +88 e. -127 f. -16 g. 32 h. -128

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Transcribed Image Text: 5. Show how each of the following signed, decimal integers would be stored in 8-bit two's complement code. Give your answer in hexadecimal. a. +100 b. -1 C. -10 d. +88 e. -127 f. -16 g. 32 h. -128
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Transcribed Image Text: 5. Show how each of the following signed, decimal integers would be stored in 8-bit two's complement code. Give your answer in hexadecimal. a. +100 b. -1 C. -10 d. +88 e. -127 f. -16 g. 32 h. -128
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a) 100 100 Since this is a positive number. we can directly convert this into binary Divide 100 successively by 2 until the quotient is 0     > 100/2 = 50, remainder is 0     > 50/2 = 25, remainder is 0     > 25/2 = 12, remainder is 1     > 12/2 = 6, remainder is 0     > 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 1100100 So, 100 of decimal is 1100100 in binary so, 100 in 2's complement binary is 01100100 Converting 01100100 to hexadecimal 0110 => 6 0100 => 4 So, in hexadecimal 01100100 is 0x64 Answer: 0x64 b) -1 -1 This is negative. so, follow these steps to convert this into a 2's complement binary Step 1: Divide 1 successively by 2 until the quotient is 0     > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 1 So, 1 of decimal is 1 in binary So, 1 in normal binary is 00000001 Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.     00000001 is flipped to 11111110 Step 3:. Add 1 to above result 11111110 + 1 = 11111111 so, -1 in 2's complement binary is 11111111 Converting 11111111 to hexadecimal 1111 => F 1111 => F So, in hexadecimal 11111111 is 0xFF Answer: 0xFF c) -10 -10 This is negative. so, follow these steps to convert this into a 2's complement binary Step 1: Divide 10 successively by 2 until the quotient is 0     > 10/2 = 5, remainder is 0     > 5/2 = 2, remainder is 1     > 2/2 = 1, remainder is 0     > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 1010 So, 10 of decimal is 1010 in binary So, 10 in normal binary is 00001010 Step 2: flip all the bits. Flip all 0's to 1 and all 1's to 0.     00001010 is flipped to 11110101 Step 3:. Add 1 to above result 11110101 + 1 = 11110110 so, -10 in 2's complement binary is 11110110 Converting 11110110 to hexadecimal 1111 => F 0110 => 6 So, in hexadecimal 11110110 is 0xF6 Answer: 0xF6 d) 88 88 Since this is a positive number. we can directly convert this into binary Divide 88 successively by 2 until the quotient is 0     > 88/2 = 44, remainder is 0     > 44/2 = 22, remainder is 0     > 22/2 = 11, remainder is 0     > 11/2 = 5, remainder is 1     > 5/2 = 2, remainder is 1     > 2/2 = 1, remainder is 0     > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 1011000 So, 88 of decimal is 1011000 in binary so, 88 in 2's complement binary is 01011000 Converting 01011000 to hexadecimal 0101 => 5 1000 => 8 So, in hexadecimal 01011000 is 0x58 Answer: 0x58 e) -127 -127 This is negative. so, follow these steps to convert this into a 2's complement binary Step 1: Divide 127 successively by 2 until the quotient is 0     > 127/2 = 63, remainder is 1     > 63/2 = 31, remainder is 1     > 31/2 = 15, remainder is 1     > 15/2 = 7, remainder is 1     > 7/2 = 3, remainder is 1  &#16 ... See the full answer