# F451 Understanding Twos Complement and Sign & Magnitude:

A PDF I made to explain Two's Complement and Sign & Magnitude.

- Created by: Jonathan
- Created on: 23-05-12 14:08

First 243 words of the document:

Understanding Two's Complement and Sign & Magnitude:

You need to know what these are so that you can perform equations with binary numbers.

MSB = Most Significant Bit, this is the bit which determines whether it is +ve or -ve

Two's Complement is a way of displaying negative numbers:

-128 64 32 16 8 4 2 1

+117 does not need to use the MSB (-128) so it is written as 01110101

However,

-117 does need to use the MSB so it is written as 10001011

-117 = -128 + 11

-128 + (8+2+1) = -117

One way of calculating the two's compliment value of a negative number is shown above, however

there is a nice algorithm which most people find easier:

- Work out the binary value of the positive number (make sure you write down the whole

number including leading zeros)

- Flip all the digits i.e. 0 for 1 and 1 for 0

- Add 1

Example: -117

Stage 1, 01110101

Stage 2, 10001010

Stage 3, 10001011

This is the same value we got for the other method

Sign and Magnitude

The MSB is 0 for a +ve and 1 for a ve, this replaces the first 0/1 which was previously 128

Therefore:

+117 = 01110101 and -117 = 11110101

Only 7 of the bits of data actually store this size of the integer. The 8th is reserved for +ve or ve

#NOTE: You will be told which form the binary is in in the exam.#

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