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For each of the following parts, determine if overflow occurs (assume values are 6-bit fixed-point binary numbers):  0001.01+1001.01   1101.10+1100.01   1000.10+1111.01   0011.10+0100.11   1000.01+0111.11

Question

For each of the following parts, determine if overflow occurs (assume values are 6-bit fixed-point binary numbers):  0001.01+1001.01   1101.10+1100.01   1000.10+1111.01   0011.10+0100.11   1000.01+0111.11

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Solution

Sure, let's go through each of these step by step:

  1. 0001.01 + 1001.01: In binary, 0001.01 is 1.25 in decimal and 1001.01 is -6.75 in decimal (as the leftmost bit is a sign bit). The sum is -5.5, which can be represented in 6-bit fixed-point binary numbers. So, no overflow occurs.

  2. 1101.10 + 1100.01: In binary, 1101.10 is -2.5 in decimal and 1100.01 is -3.75 in decimal. The sum is -6.25, which can be represented in 6-bit fixed-point binary numbers. So, no overflow occurs.

  3. 1000.10 + 1111.01: In binary, 1000.10 is -7.5 in decimal and 1111.01 is -0.75 in decimal. The sum is -8.25, which cannot be represented in 6-bit fixed-point binary numbers. So, overflow occurs.

  4. 0011.10 + 0100.11: In binary, 0011.10 is 3.75 in decimal and 0100.11 is 4.75 in decimal. The sum is 8.5, which cannot be represented in 6-bit fixed-point binary numbers. So, overflow occurs.

  5. 1000.01 + 0111.11: In binary, 1000.01 is -7.75 in decimal and 0111.11 is 7.75 in decimal. The sum is 0, which can be represented in 6-bit fixed-point binary numbers. So, no overflow occurs.

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