Skip to content

VLSIFacts

Let's Program the Transistors

  • Home
  • DHD
    • Digital Electronics
    • Fault Tolerant System Design
    • TLM
    • Verification
    • Verilog
    • VHDL
    • Xilinx
  • Embedded System
    • 8085 uP
    • 8086 uP
    • 8051 uC
  • VLSI Technology
    • Analog Electronics
    • Memory Devices
    • VLSI Circuits
  • Interview
    • Interview Experience
    • Training Experience
    • Question Bank
  • Notifications
  • QUIZ
  • Community
  • Job Board
  • Contact Us

Addition of 1’s Complement Signed Binary Numbers

Posted on March 10, 2023June 19, 2025 By vlsifacts 1 Comment on Addition of 1’s Complement Signed Binary Numbers

In an earlier article, we learned about 2’s complement addition. In this article, we will discuss how to perform 1’s complement addition. We will consider the same example that is taken for the 2’s complement addition.

Important Rule: Add the two numbers using the basic rules of binary addition. If there is a carry out of the MSB, then discard the carry, and add ‘1’ to the result.

We have considered 8-bit signed binary numbers (1 bit for sign and 7 bits for magnitude) for our example. The addend, augend, and the Sum are represented in 1’s complement form.

Both the numbers are positive

Example: 8 + 5 = ?

1’s complement representation of 8 = 00001000

1’s complement representation of 5 = 00000101

Since 8 and 5 are positive, so their 1’complement representation will be the same as its true (uncomplemented) form.

Example of 1’s complement addition for both the numbers positive

The resultant sum is a positive number.

Negative number with smaller magnitude than the positive number

Example: 8 + (-5) = ?

This example can also be read as a subtraction problem, that is 8 – 5 = ?

1’s complement representation of 8 = 00001000

1’s complement representation of -5 = 11111010

Example of 1’s complement addition for small number negative and large number positive

The resultant sum is a positive number.

Negative number with larger magnitude than the positive number

Example: -8 + 5 = ?

1’s complement representation of -8 = 11110111

1’s complement representation of 5 = 00000101

Example of 1’s complement addition for small number positive and large number negative

The resultant sum is a negative number.

Both the numbers are negative

Example: -8 + (-5) = ?

1’s complement representation of -8 = 11110111

1’s complement representation of -5 = 11111010

Example of 1’s complement addition for both the numbers negative

The resultant sum is a negative number.

The examples taken in this article are carefully chosen so that the overflow condition does not arise. Overflow occurs if the carries into and out of MSB are different. Overflow, in the case of signed binary arithmetic, is an unwanted condition, as it results in an incorrect sum. Thus, it is important to learn about Overflow and how to avoid it.

Previous           Table of Content           Next

Spread the Word

  • Click to share on Facebook (Opens in new window) Facebook
  • Click to share on X (Opens in new window) X
  • Click to share on LinkedIn (Opens in new window) LinkedIn
  • Click to share on Pinterest (Opens in new window) Pinterest
  • Click to share on Tumblr (Opens in new window) Tumblr
  • Click to share on Pocket (Opens in new window) Pocket
  • Click to share on Reddit (Opens in new window) Reddit
  • Click to email a link to a friend (Opens in new window) Email
  • Click to print (Opens in new window) Print

Like this:

Like Loading...

Related posts:

  1. What is Overflow in case of Binary Arithmetic
  2. Addition of 2’s Complement Signed Binary Numbers
  3. Understanding Overflow through Examples
  4. Range of Signed Numbers
Digital Electronics Tags:Addition of 1s complement, Carry, Overflow, Signed Number, Signed Number Arithmetic

Post navigation

Previous Post: What is Overflow in case of Binary Arithmetic
Next Post: Range of Signed Numbers

Comment (1) on “Addition of 1’s Complement Signed Binary Numbers”

  1. sharif says:
    September 12, 2023 at 3:01 pm

    Example: 8 + (-5) = ?

    This example can also be read as a subtraction problem, that is 8 – 5 = ?

    1’s complement representation of 8 = 00001000

    1’s complement representation of -5 = 11111010 wrong

    1’s complement representation of -5 = 11111011 right

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Top Posts & Pages

  • ASCII Code
  • Circuit Design of a 4-bit Binary Counter Using D Flip-flops
  • AND and OR gate using CMOS Technology
  • NAND and NOR gate using CMOS Technology
  • Texas Instruments Question Bank Part-1

Copyright © 2025 VLSIFacts.

Powered by PressBook WordPress theme

Subscribe to Our Newsletter

%d