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# System prepended metadata

title: 'Week 1: How Computers Store Negative Numbers (Using -11 as a case study)'

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**HOW COMPUTERS STORE NEGATIVE NUMBER(Using -11 as a Case Study)**
By *Akinlade Temitope Victory*

Computers use binary to represent all data, including negative numbers. Since binary is inherently positive (composed of only 1s and 0s), special methods are used to represent negative values. Three common methods are: Sign and Magnitude, One’s Complement, and Two’s Complement.

1. SIGN AND MAGNITUDE
In the Sign and Magnitude method, an 8-bit binary number is divided into two parts:

Sign Bit (Most Significant Bit):
0 indicates a positive number
1 indicates a negative number
Magnitude: The remaining 7 bits represent the absolute value of the number in binary.
Example Using -11:

Sign Bit = 1 (indicates negative)
Magnitude = Binary of 11 = 0001011
Final Binary (Sign + Magnitude) = 1 0001011 → 10001011


 2. ONE'S COMPLEMENT
One’s Complement is formed by flipping every bit of the positive binary value, changing 0s to 1s and 1s to 0s.

Example Using -11:

Binary of +11 (in 8-bit form): 00001011
Flip each bit: 11110100
One’s Complement of -11 = 11110100


3. TWO'S COMPLEMENT(Most Widely Used)
This is the most efficient and common method used in modern computing for representing negative integers and like one's complement, it's formed by flipping every bit of the positive binary value of a number but then adding 1 to it to get the nagative value.

Steps to Convert -11 into Two’s Complement:

Start with the binary of +11:
00001011
Flip all bits (One’s Complement):
11110100
Add 1 to the flipped result:
11110100 + 1 = 11110101
Final Two’s Complement for -11: 11110101

Equivalent Hexadecimal: 0xF5

**Conclusion**
Among all methods, Two’s Complement stands out due to its simplicity and efficiency. Unlike Sign and Magnitude or One’s Complement, which have two representations for zero (e.g., 00000000 and 10000000), Two’s Complement has only one zero: 00000000. This makes arithmetic operations simpler and eliminates redundancy, making it the standard in nearly all modern computing systems.