二进制编码概要.pptVIP

Exercise before class： 1、If 1810=000100102 , Write the 8-bit two’s-complement representation for the decimal number: -1810=( )2 2、Write the signed-magnitude, two’s-complement, and ones’-complement representations for each of these decimal numbers，use the bits as least: +115, -49. 3、If 100111012 is the 2’s complement representation,what is its decimal representation? 4、 Write the 8-bit signed-magnitude, two’s-complement, and ones’-complement representations for the decimal numbers: -24 10 1、已知：1810=000100102 求其相反数的补码表示： -1810=( )2 2、用最少位数写出-4910的二进制原码、补码、反码表示。1110001,1001111，1001110 3、已知：100111012是某个数的补码表示，问其用十进制的表达为？ -99 4、分别以符号-数值数制、反码、补码将-24表示为一个8位数11100111 Review of last class Operations for unsigned numbers(Addition, Multiplication, subtraction) Representation of Negative Numbers Signed-Magnitude Representation MSB as the Sign bit (0 = plus, 1 = minus) Zero? n-bit range ? When A=B,A-B=？ Complement Number Systems radix – Complement, Diminished Radix – Complement r’s complement= r n –D= (r n -1–D)+1 MSB (the sign bit) ,Weight of the MSB?, range of representable numbers ? Sign extension Signed-Magnitude system ？Two’s-complement number system? Sum up for the Complement (总结) 1.Positive number has the same： Sign-Magnitude, Ones’ – Complement, and Two’s- Complement ( 正数的原码、反码、补码相同) 2. MSB (the sign bit) : 1 =minus; 0=plus Weight of the MSB: -2n-1 2.6 Two’s – Complement Addition  and Subtraction (二进制补码的加法和减法) we define [x] to be the two’s complement representation of x [x + y] = ( [x] + [y] ) [x - y] = ( [x] + [-y] ) 4 bits binary number 0000，0001，0010，0011， 0100, 0101， 0110, 0111, 1000, 1001， 1010，1011， 1100, 1101， 1110, 1111,  We can added +n to that number by counting up n times, that is, b