Signed and Unsigned Numbers

A binary number may be positive or negative. Generally, we use the symbol “+” and “-” to represent positive and negative numbers, respectively. The sign of a binary number has to be represented using 0 and 1, in the computer. An n-bit signed binary number consists of two parts – sign bit and magnitude. The left most bit, also called the Most Significant Bit (MSB) is the sign bit. The remaining n-1 bits denote the magnitude of the number.

In signed binary numbers, the sign bit is 0 for a positive number and 1 for a negative number. For example, 01100011 is a positive number since its sign bit is 0, and, 11001011 is a negative number since its sign bit is 1. An 8-bit signed number can represent data in the range -128 to +127 (-2⁷ to +2⁷-1). The leftmost bit is the sign bit.

In an n-bit unsigned binary number, the magnitude of the number n is stored in n bits. An 8-bit unsigned number can represent data in the range 0 to 255 (2⁸= 256).

Complement of Binary Numbers

Complements are used in computer for the simplification of the subtraction operation. We now see, how to find the complement of a binary number. There are two types of complements for the binary number system – 1’s complement and 2’s complement.

• 1’s complement of Binary number is computed by changing the bits 1 to 0 and the bits 0 to 1. For example,
• 2’s complement of Binary number is computed by adding 1 to the 1’s complement of the binary number. For example,
• 1’s complement of 110 is 001
• 1’s complement of 1011 is 0100
• 1’s complement of 1101111 is 0010000
• 2’s complement of 110 is 001 + 1 = 010
• 2’s complement of 1011 is 0100 + 1 = 0101
• 2’s complement of 1101111 is 0010000 + 1 = 0010001