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. -74

a) Convert the following decimal values to 8-bit 2's complement representation:

i. -92

1. Convert 92 to binary: 92 in binary is 01011100.
2. Find the 1's complement (invert the bits): 10100011.
3. Add 1 to the 1's complement: 10100011 + 1 = 10100100.
4. Therefore, -92 in 8-bit 2's complement is 10100100.

ii. -36

1. Convert 36 to binary: 36 in binary is 00100100.
2. Find the 1's complement (invert the bits): 11011011.
3. Add 1 to the 1's complement: 11011011 + 1 = 11011100.
4. Therefore, -36 in 8-bit 2's complement is 11011100.

b) Perform the following conversions:

i. 1100011₂ converts into a decimal number system

1. Identify the binary number: 1100011.
2. Convert to decimal: (1 * 2^6) + (1 * 2^5) + (0 * 2^4) + (0 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0).
3. Calculate: 64 + 32 + 0 + 0 + 0 + 2 + 1 = 99.
4. Therefore, 1100011₂ in decimal is 99.

ii. 1011111₂ converts into a decimal number system

1. Identify the binary number: 1011111.
2. Convert to decimal: (1 * 2^6) + (0 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (1 * 2^1) + (1 * 2^0).
3. Calculate: 64 + 0 + 16 + 8 + 4 + 2 + 1 = 95.
4. Therefore, 1011111₂ in decimal is 95.

c) Convert the following decimal values to a 12-bit 2's complement representation:

i. -189

1. Convert 189 to binary: 189 in binary is 10111101.
2. Extend to 12 bits: 000010111101.
3. Find the 1's complement (invert the bits): 111101000010.
4. Add 1 to the 1's complement: 111101000010 + 1 = 111101000011.
5. Therefore, -189 in 12-bit 2's complement is 111101000011.

ii. -74

1. Convert 74 to binary: 74 in binary is 01001010.
2. Extend to 12 bits: 000001001010.
3. Find the 1's complement (invert the bits): 111110110101.
4. Add 1 to the 1's complement: 111110110101 + 1 = 111110110110.
5. Therefore, -74 in 12-bit 2's complement is 111110110110.