Binary math

Question 1

Perform the following binary additions: 1. 101 + 11 = 2. 111 + 111 = 3. 1010 + 1010 = 4. 11101 + 1010 = 5. 11111 + 11111 =

TipSolution

1. 1000
2. 1110
3. 10100
4. 100111
5. 111110

Question 2

Convert the following numbers to binary and perform the operation: 1. (32)₁₀ = 2. (50)₁₀ + (32)₁₀ =  3. (64)₁₀ + (4)₁₀ = 4. (100)₁₀ + (220)₁₀ =

TipSolution

1. 100000
2. 1010010
3. 1000100
4. 101000000

Question 3

Given the codebook below, write the binary instructions to perform this operation: (100)₁₀ + (220)₁₀ . - What’s the final value on the External Data Bus?

TipSolution

1. 1000 0000
2. 0110 1110
3. 1001 0000
4. 1101 1100
5. 1011 0000
6. 1100 0000

1101110 + 11011100 = 101000000, but since the CPU’s bus size is limited to 8 bits, the most significant bit (left most, or highest power) will be lost. The final answer on the ESD is 01000000 (64).

Question 4

What is -230 in two’s complement represetation with an 12 bits bus width?

TipSolution

1. Write 230 in binary: 1 0100 0000
2. Complete the number of bits to 12 and add a bit for the sign: __0__0001 0100 0000
3. Flip the bits (one’s complement): __1__1110 1011 1111
4. Add 1 to get two’s complement: __1__1110 1100 0000

Question 5

Convert the following numbers to binary and perform the operation on an 8-bit CPU: 1. (50)₁₀ - (32)₁₀ =  2. (64)₁₀ - (4)₁₀ = 3. (100)₁₀ - (120)₁₀ =

TipSolution

1. (50)₁₀ - (32)₁₀ = (50)₁₀ + (-32)₁₀ Binary 50: 0011 0010 Binary 32: 0010 0000 Invert 32: 1101 1111 Add 1: 1110 0000 Operation: 50-32 : 0011 0010

• 1110 0000

  0001 0010

2. (64)₁₀ - (4)₁₀ = (64)₁₀ + (-4)₁₀ Binary 64: 0100 0000 Binary 4: 0000 0100 Invert 4: 1111 1011 Add 1: 1111 1100 Operation 64 - 4: 0100 0000

• 1111 1100

  0011 1100

3. Binary 100: 0110 0100 Binary 120: 0111 1000 Invert 120: 1000 0111 Add 1: 1000 1000 Operation: 100 - 120: 0110 0100

• 1000 1000
  1110 1100 (-20)