where do we use the binary number system
Binary number The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices.
Signed number representations This representation is also called "sign–magnitude" or "sign and magnitude" representation. In this approach, the problem of representing a number's sign can be to allocate one sign bit to represent the sign: setting that bit (often the most significant bit) to 0 is for a positive number or positive zero, and setting it to 1 is for a negative number or negative zero. The remaining bits in the number indicate the magnitude (or absolute value). Hence, in a byte with only seven bits (apart from the sign bit), the magnitude can range from 0000000 (0) to 1111111 (127). Thus numbers ranging from −12710 to +12710 can be represented once the sign bit (the eighth bit) is added. For example, −4310 encoded in an eight-bit byte is 10101011 while 4310 is 00101011. A consequence of using signed magnitude representation is that there are two ways to represent zero, 00000000 (0) and 10000000 (−0).