Negative Numbers in Binary
Date: 08/19/99 at 17:06:35 From: Ramesh Akella Subject: Binary Number How do I represent -53 as a binary number? Is it 110101? Wouldn't that be +53? Can you help me?
Date: 08/19/99 at 22:58:21 From: Doctor Peterson Subject: Re: Binary Number Hi, Ramesh. Mathematically, there's nothing wrong with writing -53 as -110101, using a separate negative sign as we do in decimal. In computers, the usual method for storing signed numbers is called "twos-complement": to negate a number, you take the complement (changing 0 to 1 and 1 to 0) and add 1: 53 --> 00110101 -53 --> 11001010 + 1 = 11001011 Since any negative number has the leftmost bit set, the effect of this is to take the upper half of the range of numbers that can be stored in a fixed number of bits (eight bits in my example) and use them for negative numbers. The numbers 0 to 127 are positive; numbers 128 to 255 represent -128 to -1. You can still add two numbers just as you do with unsigned numbers: -53 = 11001011 + 63 = 00111111 ----- ----------- 10 = (1)00001010 In this case an extra carry digit is generated, but it is ignored and the result is the correct answer. You can learn more about this by using a searcher like Google (http://www.google.com/) to look for the phrase "twos complement." - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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