Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Binary Real Numbers Conversion Real numbers are decimal numbers. In programming we often use a Float data type to represent these. Real numbers are stored using a sign bit, an exponent section and a mantissa. The way these work vary from system to system. Exam method: In an exam you need to be able to convert from binary to a denary real number and vice-versa using this method: Place value . 1/2 1/4 1/8 1/16 1/32 4s 2s 1s - 0.5 0.25 0.125 0.0625 0.03125 1 0 1 . 1 1 0 1 0 The numbers before the decimal place act as regular binary numbers with 4s, 2s and 1s. The numbers after the decimal place start with the ½s, then the ¼s and so on. This allows you to build up the decimal part of the number by using the fractions. Build up each part of the number to convert to denary: • left side = one 4, no 2, one 1 = 4 + 0 + 1 = 5 • right side = one half, one quarter, one sixteenth = 0.5 + 0.25 + 0.0625 = 0.8125 • combine = left side . right side = 5.8125 Questions: a) Complete the table to show the unshaded place values and then convert the binary real number shown to denary. Place value = 3.75 4s 2s 1s - 0.5 0.25 0 1 1 . 1 1 0 0 0 b) Complete the table to show the unshaded place values and then convert the binary real number shown to denary. Place value 4s 2s 1s - 0.5 0.25 0.125 0 1 0 . 0 1 1 0 0 0 0 0 = 2.375 c) Convert the binary real number shown below to denary. 1 1 1 . 1 0 = 7.5 Converting to binary real numbers: To convert from denary to binary simply break the number down into the two parts and build each of them up using the place values. • 1.25 is split into 1 and .25 • 1 goes on the left side as 001 • on the right side, 0.25 is made up of one quarter, so the right side is 01000 Questions: a) Convert the denary real number 2.5 to binary by completing the table. 0 1 0 . 1 0 0 0 0 b) Convert the denary real number 7.75 to binary by completing the table. 1 1 1 . 1 1 0 0 0 c) Convert the denary real number 2 ⅝ to binary by completing the table. 0 1 0 . 1 0 1 0 d) Convert the denary real number 3.5 to binary using a standard place value notation with 3 bits before the decimal place. = 011.1 (you don't need the end 0s) 0