Arithmetic for Computers (Number Systems and Operations) by Chong Kit Shing B031310164

Two’s Complement (2’s complement)

Two’s complement  solve  the problem of alternate representation of zeros. The 2’s complement representation used for sign and magnitude number can be determined. Assume a microprocessor has 8 register bits. Figure 1.1 shows the sign bits or the most significant bit(MSB). If the bit is 0, then the number is positive (+). Conversely, if the MSB is 1, then the number is negative (-). The others remaining 7 bits are represent as the magnitude numbers. The first bit from right is a least significant bit (LSB).  Creating the two’s complement of a number begins by flipping all the bits, as with one’s complement, but then 1 is added to the result.

IEEE Floating Point

The Institute of Electronic and Electrical Engineers (IEEE) has proposed a standard for floating point arithmetic on small computers. A single-precision floating point number that follows the IEEE standard has 1 sign bit, and 8 bit exponent, and 23 bits for the mantissa. A double-precision floating point number that follows the IEEE standard has 1 sign bit, and 11 bit exponent, and 52 bits for the mantissa.