Oppiskele Two's Complement Representation | Binary Representation and Two’s Complement

Understanding how computers represent negative numbers is crucial when working with low-level programming in C.

The most common way to represent signed integers is two's complement. In this system, the most significant bit (MSB) is the sign bit: 0 means non-negative, 1 means negative. Negative numbers are formed by inverting all bits of the positive value and adding 1.

Two’s complement allows addition and subtraction to work the same way for both positive and negative numbers, which simplifies hardware design and arithmetic operations in software.

twos_complement_demo.c


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#include <stdio.h>
#include <stdint.h>

void print_binary(uint8_t value) {
    for (int i = 7; i >= 0; i--) {
        printf("%d", (value >> i) & 1);
    }
    printf("\n");
}

int main(void) {
    int8_t positive = 25;
    int8_t negative = (int8_t)(~positive + 1); // two's complement

    printf("Positive value: %d\n", positive);
    printf("Binary: ");
    print_binary((uint8_t)positive);

    printf("\nNegative value: %d\n", negative);
    printf("Binary: ");
    print_binary((uint8_t)negative);

    return 0;
}

To convert a positive number to its two’s complement, start with the value, for example 25. First, invert all its bits using the bitwise NOT operator (~). Then add 1 to the result. This produces the binary representation of -25.

When you print both values in binary, you can see how two’s complement allows the same arithmetic logic to work for positive and negative numbers, with carries and borrows handled automatically.

Note

Two's complement is used by most modern systems, which is why signed integer arithmetic works consistently at both the hardware and software levels.

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Suggested prompts:

Can you explain why two's complement is preferred over other methods for representing negative numbers?

How does the bitwise NOT operator work in C?

Can you show an example of converting a number to two's complement in C?

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