Convert the following decimal values to 8-bit 2's complement representation(1*2 Marks)i. -92ii. -36c) Perform the following conversions. (1*2 Marks)i. 11000112 converts into a decimal number systemii. 10111112. converts into a decimal number systemd) Convert the following decimal values to a 12-bit 2's complement representation.(1*2 Marks)i. -189ii. -749e) Convert the following decimal values to a 16-bit 2's complement representation. (1*2Marks)i. -2342ii. 234
Question
Convert the following decimal values to 8-bit 2's complement representation(12 Marks)i. -92ii. -36c) Perform the following conversions. (12 Marks)i. 11000112 converts into a decimal number systemii. 10111112. converts into a decimal number systemd) Convert the following decimal values to a 12-bit 2's complement representation.(12 Marks)i. -189ii. -749e) Convert the following decimal values to a 16-bit 2's complement representation. (12Marks)i. -2342ii. 234
Solution
i. To convert -92 to 8-bit 2's complement representation:
- Convert 92 to binary: 01011100
- Invert the bits: 10100011
- Add 1 to the result: 10100100
ii. To convert -36 to 8-bit 2's complement representation:
- Convert 36 to binary: 00100100
- Invert the bits: 11011011
- Add 1 to the result: 11011100
c) i. To convert 11000112 to decimal:
- Multiply each bit by 2 raised to the power of its position, starting from 0 at the rightmost bit: (12^6) + (12^5) + (02^4) + (02^3) + (02^2) + (12^1) + (1*2^0) = 103
ii. To convert 10111112 to decimal:
- Multiply each bit by 2 raised to the power of its position, starting from 0 at the rightmost bit: (12^6) + (02^5) + (12^4) + (12^3) + (12^2) + (12^1) + (0*2^0) = 94
d) i. To convert -189 to 12-bit 2's complement representation:
- Convert 189 to binary: 000010111101
- Invert the bits: 111101000010
- Add 1 to the result: 111101000011
ii. To convert -749 to 12-bit 2's complement representation:
- Convert 749 to binary: 001011111101
- Invert the bits: 110100000010
- Add 1 to the result: 110100000011
e) i. To convert -2342 to 16-bit 2's complement representation:
- Convert 2342 to binary: 0000100100011110
- Invert the bits: 1111011011100001
- Add 1 to the result: 1111011011100010
ii. To convert 234 to 16-bit binary:
- Convert 234 to binary: 0000000011101010
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