Base2Note: Due to the limited precision of numbers stored in spreadsheets, really large numbers are unlikely to be exact.01122438416532664712882569512101024112048124096138192141638415327681665536171310721826214419524288201048576212097152224194304238388608241677721625335544322667108864271342177282826843545629536870912301073741824312147483648324294967296338589934592341717986918435343597383683668719476736371374389534723827487790694439549755813888401099511627776Base2Conversion by multiplication of powers of the base.Input11111011101PowersBit "contribution"0111112000241143811841611165320006641164712811128825611256951211512101024111024112048000Base 10 Output2013Input2013Base2Conversion by iterative division02013110061125030032511141251156211631007151187119311101111101112000011111011101Increment and Decrement00000IncrementIf bit input and carry input are not equal, bit output is one. If bit input and carry input are both one, carry output is one.000000000110001DecrementIf bit input and borrow input are not equal, bit output is one. If bit input is zero and borrow input is one, borrow output is one.0000011111151111Set 1 to increment1000000000110001701signed magnitude-71111The first bit indicates the sign. You must check the sign, before incrementing or decrementing to see if magnitude should be incremented or decremented. If incrementing, must check if number is -1. If decrementing, must check if number is 0. Be careful about +0 and -0.one's complement-71000Negate all bits to indicate a negative number. Incrementing -1 without check gives -0. Incrementing -0 and decrementing +0 require correction. Be careful about +0 and -0.two's complement-710010001Increment and decrement in same manner as unsigned numbers. There are more negative numbers than positive numbers.Overflow can occur with all three representations!11109876543210input2013test sign2013+convert absolute value011111011101ones' complement2013011111011101two's complement201301111101110112-bit two complementInput100000100011PowersBit "contribution"011112122400380041600532132664007128008256009512001010240011-20481-2048Base 10 Output-2013Word Sizen16Number of possible values2n65536Unsigned numbersLargest number2n - 165535Smallest number00Twos-complement numbersLargest number2n-1 - 132767Smallest number- 2n-1-3276811109876543210input-10910010011signed extension-10911111001001111109876543210Unsigned AdditionThe carries0000000010000Term 1101012447Term 20101040The result1001101101112487Overflows occurs when the true result would exceed the capacity of the word. In this case, the carry-out of the addition will be 1. Also, the result would be less than one of the numbers being added.11109876543210Twos-Complement AdditionThe carries0100111000000Term 1010101776Term 20101010101066The result101100011010-1254Overflows occurs when the true result would be outside the allowed range of the word size. In this case, the carry-out and carry-in of the leftmost bit additional are unequal. Overflow can never occur when adding numbers with different signs. Overflow occurs only when two numbers of the same sign are added and the result is of the other sign.11109876543210Ones-Complement AdditionThe carries1111000000000Term 11010-55Term 210101-200First result111011111111-256More carries0000111111111Result111100000000-255SE7E6E5E4E3E2E1E0F22F21F20F19F18F17F16F15F14F13F12F11F10F9F8F7F6F5F4F3F2F1F0010101101010raw bitsraw meaningsSign0Sign+Exp137Exp10Frac8101888Frac0.96582multipliersSign1Exp1024.000000000Frac1.965820313Total2013.000000000Input12.58Whole12Fraction0.5800.16110.32020.64030.28140.56050.12160.24070.48080.96090.921100.841110.681120.361.1001010001111normalizationwholefractionpowermultiplierproduct17010001.0100.06250000000117.06380001000.10001000000.53125000001217.06340000100.01000100000.26562500002417.06320000010.00100010000.13281250003817.06310000001.00010001000.066406250041617.06310000001.00010001000.066406250041617.06310000001.00010001000.066406250041617.063127excess-127131Truth TableX & YX | Y~ XX ^ YXYX AND YX OR YNOT XX XOR Y0001001011110010111100clear or set?CSSSCinput1010to clear1110001110003640mask1011111111013069with and1010001110002616to set1110001110003640mask001010010000656with or1110101110003768ASCII0011223344556677000nul10dle20sp30040@50P60`70p101soh11dc121!31141A51Q61a71q202stx12dc222"32242B52R62b72r303etx13dc323#33343C53S63c73s404eot14dc424$34444D54T64d74t505enq15nak25%35545E55U65e75u606ack16syn26&36646F56V66f76v707bel17etb27'37747G57W67g77w808bs18can28(38848H58X68h78x909ht19em29)39949I59Y69i79y100Anl1Asub2A*3A:4AJ5AZ6Aj7Az110Bvt1Besc2B+3B;4BK5B[6Bk7B{120Cnp1Cfs2C,3C<4CL5C\6Cl7C|130Dcr1Dgs2D-3D=4DM5D]6Dm7D}140Eso1Ers2E.3E>4EN5E^6En7E~150Fsi1Fus2F/3F?4FO5F_6Fo7FdelUTF-8Input2012Raw binary83886084194304209715210485765242882621441310726553632768163848192409620481024512256128643216842111111011100UTF-8 binary1101111110011100��