Question

1. Convert a 10 digit binary number that has 3 decimal digits (of your own choosing) to decimal (show all steps) .
2. Find the twos complement of the following number: (show all steps) 88 decimals (first convert to binary)

Answer 1

Converting Binary to Decimal

Convert binary to decimal using Positional Notation

Since number numbers are type of positional number system. That means weight of the positions from right to left are as 2⁰, 2¹, 2², 2³... and so on for the integer part and weight of the positions from left to right are as 2^-1, 2^-2, 2^-3, 2^-4... and so on for the fractional part.

I am taking a 3 decimal digit number 618

1001101010

2⁹ x 1 + 2⁸ x 0 + 2⁷ x 0 + 2⁶ x 1 + 2⁵ x 1 + 2⁴ x 0 + 2³ x 1 + 2² x 0 + 2¹ x 1 + 2⁰ x 0

= 512 + 64 + 32 + 8 + 2

= 618

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Finding two's complement of a number

To get 2’s complement of binary number is 1’s complement of given number plus 1 to the least significant bit (LSB).

For example 2’s complement of binary number 10010 is (01101) + 1 = 01110.

Given number 88.

Convert it into binary

|_88_____
2|_44 - 0
2|_22 - 0
2|_11 - 0
2|_5 - 1
2|_2 - 1
2|_1 - 0

The binary is 1011000

First find 1's complement of binary number

1's complement is convert all 0 to 1 and 1 to 0.

Therefore 1's complement of 1011000 is 0100111

Then add 1 to the 1's complement

(0100111) + 1 = 0101000

Thank you. Please ask me if you have any doubt.