In: Computer Science
a newer version of IEEE 754 defines a half precision floating point format that is only 16 bits wide. the left most bit is still the sign bit. the exponent is 5 bits wide and has a bias of 15, and the fraction is 10 bits long. A hidden 1 is assumed similar to single and double precision formats. what is the bit pattern to represent -0.5 using this format?
1011100000000000 Explanation: ------------- -0.5 Converting 0.5 to binary Convert decimal part first, then the fractional part > First convert 0 to binary Divide 0 successively by 2 until the quotient is 0 Read remainders from the bottom to top as So, 0 of decimal is in binary > Now, Convert 0.50000000 to binary > Multiply 0.50000000 with 2. Since 1.00000000 is >= 1. then add 1 to result > This is equal to 1, so, stop calculating 0.5 of decimal is .1 in binary so, 0.5 in binary is 00000000.1 -0.5 in simple binary => .1 so, -0.5 in normal binary is .1 => 1. * 2^-1 16-bit format: -------------------- sign bit is 1(-ve) exponent bits are (15-1=14) => 01110 Divide 14 successively by 2 until the quotient is 0 > 14/2 = 7, remainder is 0 > 7/2 = 3, remainder is 1 > 3/2 = 1, remainder is 1 > 1/2 = 0, remainder is 1 Read remainders from the bottom to top as 1110 So, 14 of decimal is 1110 in binary frac/significant bits are 0000000000 so, -0.5 in 16-bit format is 1 01110 0000000000