Representation of Signed Numbers - R.D.Sivakumar
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This document discusses the representation of signed numbers in computers. It explains two common methods: sign-magnitude representation and 2's complement representation. For 2's complement, it provides the step-by-step process to convert a positive number to its negative equivalent in binary. It also discusses interpreting numbers as signed or unsigned and how this affects comparisons. Finally, it outlines the different value ranges for unsigned versus signed integers in an n-bit system.
Representation of Signed Numbers - R.D.Sivakumar
- 1. R.D.SIVAKUMAR, M.Sc., M.Phil., M.Tech., Assistant Professor of Computer Science & Assistant Professor and Head, Department of M.Com.(CA), Ayya Nadar Janaki Ammal College, Sivakasi – 626 124. Mobile: 099440-42243 e-mail : sivamsccsit@gmail.com website: www.rdsivakumar.blogspot.in REPRESENTATION OF SIGNED NUMBERS
- 2. If computers represent non-negative integers(unsigned) only. Computers represent negative integers(signed) only. The leftmost bit is 0, the number is positive. The leftmost bit is 1, the number is negative. REPRESENTATION OF SIGNED NUMBERS Sign+magnitude representation 0100 = +4 1100 = -4 The left most bit indicate the sign “0” indicates the positive. And “1” indicates the negative.
- 3. Change every 0 to 1 and every 1 to 0 . Add 1 to the result. Taken to pad(fill with zero) the original value out to the full representation width before applying this algorithm. 8-bit representation to store the number. 2’s COMPLEMENT REPRESENTAION . The binary equivalent of 23 is 10111. Pad with zeros to make 8-bit pattern 00010111. Invert all the bits 11101000. Add 1 to the result 11101001.
- 4. Manual method to represent signed integers in 2’s complement form This is an easier approach to represent signed integers. This is for –ve numbers only. Step 1: Copy the bits from right to left, through and including the first 1. Step 2: Copy the inverse of the remaining bits. Example 1: To represent –4 in a 4-bit representation: The binary equivalent of the integer 4 is 0100 As per step1, copy the bits from right to left, through and including the first 1 => 100 As per step2, copy the inverse of the remaining bits => 1 100 => -4 Example 2: To represent –23 in a 8-bit representation: The binary equivalent of 23 is 00010111 As per step 1: 1 As per step 2: 11101001 => -23
- 5. Interpretation of unsigned and signed integers X = 1001 Y = 0011 Comparing two binary number for finding which is greater, the comparison Depends on whether the numbers are considered as signed or unsigned numbers. (X>Y) is this true or false If X is greater than Y because they are unsigned. If X is less than Y because they are signed.
- 6. Range of unsigned and signed integers . In a 4-bit system, the range of unsigned integers is from 0 to 15, that is, 0000 to 1111 in binary form. Each bit can have one of two values 0 or 1. Therefore, the total number of patterns of 4 bits will be 2 X 2 X 2 X 2 = 16. In an n-bit system, the total number of patterns will be 2n.. Hence, if n bits are used to represent an unsigned integer value, the range is from 0 to 2n-1, that is, there are 2n different values. In case of a signed integer, the most significant (left most) bit is used to represent a sign. Hence, half of the 2n patterns are used for positive values and the other half for negative values. The range of positive values is from 0 to 2n-1-1 and the range of negative values is from –1 to –2n-1. In a 4-bit system, the range of signed integers is from –8 to +7.