Question

Express the decimal number (25)₁₀ as an 8-bit unsigned binary number.

Express the decimal number (-37)₁₀ as an 8-bit sign-magnitude binary number.

Express the decimal number (-37)₁₀ as an 8-bit 1's complement binary number.

Answer 1

Answer 1 ->

Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.

• division = quotient + remainder;
• 25 ÷ 2 = 12 + 1;(LSB bit)
• 12 ÷ 2 = 6 + 0;
• 6 ÷ 2 = 3 + 0;
• 3 ÷ 2 = 1 + 1;
• 1 ÷ 2 = 0 + 1;(MSB bit)

25₍₁₀₎ = 00011001₍₂₎

Answer 2 -->

37₍₁₀₎ = 00100101₍₂₎

then sign-magnitude of -37₍₁₀₎   is 100100101₍₂₎ .

In sign magnitude represent as positive integer in binary but if number is negative then MSB bit 1 , else number is positive then MSB bit 0.

Answer 3 -->

37₍₁₀₎ = 00100101₍₂₎

To get the negative integer number representation on 8 bits, signed binary one's complement, replace all the bits on 0 with 1s and all the bits set on 1 with 0s (reverse the digits, flip the digits).

so 1's complement of 00100101₍₂₎ = 11011010₍₂₎