Question

b. 8 bit Twos Complement (Ones complement and a 1 to result

(show original = binary conversion = one’s complement = twos complement)

Examples: -0 = -0000 0000 = 1111 1111 = 0000 0000

+0 = +0000 0000 = 0000 0000 = 0000 0000

-5 =

+253 =

-87 =

-114 =

4. Convert the following Floating Point numbers to binary  

Example: 0.25 base 10 = 0.01 in base 2

0.50 base 10 =

0.125 base 10 =

0.75 base 10 =

Answer 1

The answers for your question given below

8 bit 2’s complement

To find 8 bit 2’s complement of decimal number

Step 1: Write the binary conversion of the given decimal number

Step 2: Take the 1’s complement of the binary form. For that we have to take the complement of each bit in the binary form by changing zeroes to ones and ones to zeros

Step 3: To find 2’s complement, add 1 to the 1’s complement

a) -5₁₀ = -0000 0101₂ = 1111 1010 = 1111 1011

-5 to binary = -0000 0101

1’s complement = 1111 1010

2’ complement = 1111 1010 + 1 = 1111 1011

b) +253₁₀ = we can’t calculate 8 bit 2’s complement. Decimal must be in the range of -128 to 127

c) -87₁₀ = 0101 0111₂ = 1010 1000 = 1010 1001

-87 to binary = 0101 0111

1’s complement = 1010 1000

2’ complement = 1010 1000 + 1 = 1010 1001

d) -114₁₀ = 0111 0010₂ = 1000 1101 = 1000 1110

-114 to binary = 0111 0010

1’s complement = 1000 1101

2’ complement = 1000 1101 + 1 = 1000 1110

Floating Point numbers to Binary

To find binary of floating point numbers we have to convert decimal part and fractional part to binary independently.

Decimal part conversion: Divide decimal part with 2, Remainder is saved as bit. Result is used to divide by 2 again, and it is repeated until result becomes zero. Then resulting remainder bits are calculated in reverse order.

Fractional part conversion: Multiply the fractional part with 2, Decimal part from the result is saved as bit. Remaining fractional part again multiplied with 2 until the result becomes 1. The resulting decimal bits calculated in the order they are written.

a) 0.50 base 10 = 0.1 base 2

0.50 * 2 =1

b) 0.125 base 10 = 0.001 base 2

0.125 * 2 = 0.25

0.25 * 2 = 0.5

0.5 * 2 = 1

c) 0.75 base 10 = 0.11 base 2

0.75 * 2 = 1.5

0.5 * 2 = 1