第三十六章超脫輪回(大結局)下

1、1CMSC 250Chapter 1, cont., Combinatorial circuits蒼穹龍騎蒼穹龍騎 http:/ 2CMSC 250Basic logic gateslAn and gate:lAn or gate:lA not gate:3CMSC 250Discrete StructuresCMSC 250Lecture 64CMSC 250Combining & determining I/O relationshiplFrom a circuit to a Boolean formula:lp (q r)pqr5CMSC 250Draw a circuit for:lp

2、, q & r are inputs.lSimplify before building the circuit.pqroutput111111011010100101100100001000006CMSC 250Number conversionslDifferent number system bases are used when convenient some commonly-used bases are 10 (decimal), 2 (binary), 8 (octal), 16 (hexadecimal) the base tells how many different nu

3、merals are used the base also determines the value of each placelConversions from anything to base 10 use the definition of the number systemlConversions from base 10 to anything use repeated integer division7CMSC 250Addition of binary numberslCarry if the number would be too large for the number sy

4、stem- if it is greater than 11001+101001+111011+101101+1118CMSC 250Discrete StructuresCMSC 250Lecture 79CMSC 250Addition of octal and hexadecimal numberslCarry if the number would be too large for the number system (larger than 7 or 15)7238+1282658+338ABC16+1216CDE16+ED1610CMSC 250Twos complementlTo

5、 represent negative values in binary:1. Find the binary equivalent of the absolute value.2. Pad on the left to completely fill the bits in the specified bit width3. Switch all of the 1s to 0s and 0s to 1s.4. Add 1 to the result.Example: find the 8-bit twos complement representation of -43:1. 4310 =

6、10101122. 0010101123. 1101010024. 110101012 = -431011CMSC 250Using a circuit for adding two bitslWrite as a logic expression lTranslate to circuitspqcarrysum0000010110011110inputoutput12CMSC 250Half adderp and q are binary values (1 bit each)sum = (p q) (p q)carry = (p q)qpsumcarry13CMSC 250Full add

7、er (for three bits)lp, q, and r are binary digitslp + q + r produces a sum value and a carry valuehalf-adder #1half-adder #2pqrS1C1CSC214CMSC 250Parallel adderslChain these half adders and full adders together for multi-bit additionlX1X2X3 + Y1Y2Y3 = CA1A2A3 X3Y3X2Y2X1Y1half-adderfull-adderfull-adderA3carrycarrycarryA2A115CMSC 250Discrete StructuresCMSC 250Lecture 816CMSC 250Draw a circuit for abcoutput0000 0 0 0 0 00010 0 0 0 0 10100 0 0 1 0 00110 0 1 0 0 11000 1 0 0 0 01010 1 1 0 0 11101 0 0 1 0