Книга: Introduction to Microprocessors and Microcontrollers

A quick way to find the two’s complement of a binary number

Start from the left-hand end and invert each bit until you come to the last figure 1. Don’t invert this figure and don’t invert anything after it.

Example 1

What is –24₁₀ expressed as an 8-bit two’s complement binary number?

1 Change the 24₁₀ into binary. This will be 11000.

2 Add leading zeros to make it an 8-bit number. This is now 00011000.

3 Now start inverting each bit, working from the left until we come to the last figure ‘1’. Don’t invert it, and don’t invert the three zeros that follow it.

Example 2

What is –100₁₀ expressed as a 16-bit two’s complement binary number?

1 Convert the 10010 into binary. This gives 1100100₂.

2 Add nine leading zeros to make the result the 16-bit number 0000000001100100.

3 Now, using the quick method, find the two’s complement:

The result is 1111 1111 1001 1100

Example 3

Find the value of 1011 0111₂–00 1011₂ using two’s complement addition.

1 The second number has only six bits so add two zeros on the lefthand end to give 1011 0111–0000 1011.

2 Invert each bit in the number to be subtracted to find the one’s complement. This changes the 00001011 to 11110100.

3 Add 1 to give the two’s complement: 11110100+1=11110101 (or do it the quick way).

4 Add the first number to the two’s complement of the second number:

5 The result so far is 110101100 which includes that extra carry so we cross off the msb to give the final answer of 10101100₂.

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