Question

Translate the base 10 value -45 into 8-bit two's complement representation.

Answer 1

Write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

45 /  2  result 22 remainder  1
22 /  2  result 11 remainder  0
11 /  2  result 5  remainder  1
5  /  2  result 2  remainder  1
2  /  2  result 1  remainder  0
1  /  2  result 0  remainder  1

Read the remainders from bottom to top.

( 45 )₁₀ = ( 101101 )₂

( 45 )₁₀ in 8-bit is ( 00101101 )₂

Ones complement 
= Inverting all the bits in binary
= 11010010

Twos complement 
= Ones complement + 1
= 11010010 + 1
= 11010011

11010011