计组笔记第一章个人整理未完善
计算机组成原理 笔记整理
第一章
1.1
The Three–Y’s（三个原则）
•Hierarchy（层次化）
•Modularity（模块化）
•Regularity（规整化）
Weighted positional number system(带权的位置数制)
‒Base(基数)
‒weighted(权)
binary numbers:
base:2
weighted:2^i
bits(1),bytes(8),nibbles(4)
•2^10=1 Kilo≈1000(1024≈10^3)
•2^20=1 Mega≈1 million(1,048,576≈10^6)
•2^30=1 Giga≈1 billion(1,073,741,824≈10^9)
1.2
Data types representing information in a computer
Unsigned numbers(无符号数)
•Unsigned number：are created directly as ordinary binary codes
–Operation codes in the OP code field
–Register numbers in address field
–Memory address
–counter
–Time,clock frequency
Signed numbers(有符号数)
•Fix-Point Number(小数点不占位)
•Floating-Point Number(小数点占位)
MSB: the Most Significant (left-most) Bit
Sign-Magnitude Numbers（原码）
•1 sign bit,N-1 magnitude bits
•Sign bit is the Most Significant (left-most) Bit
–Positive number: sign bit=0
–Negative number: sign bit=1
•Example,4-bit sign/mag representations of ±6:
+6=0110;
-6=1110;
[+0]=0.0000000;
[-0]=1.0000000;
•Range of an N-bit sign/magnitude number:
[-(2(N-1)-1),2(N-1)-1]
Two’s Complement Numbers（补码）
–Addition works（易于加法操作）
–Single representation for 0（0的表示是唯一的）
•正数补码：和原码一样，符号用0表示，数值用二进制表示；
•负数补码：符号用1表示，原码数值部分按位取反，末位加1;
•The Most Significant Bit still indicates the sign
•1=negative,0=positive;
•Range of an N-bit two’s comp number:
[-(2N-1),2N-1-1]
One’s Complement Numbers（反码）
The sign bit '0' is assigned as the magnitude indicator in the remaining n-1 bits.
Assign a negative sign to the '1' at the most significant bit (msb) of the one's complement of the magnitude in the remaining n-1 bits.
•Decimal：
–X1=+0.1011011,[X1]1’s compl=0.1011011
–X2=-0.1011011,[X2]1’s compl=1.0100100
•Integer：
–X3=+1011011,[X3]1’s compl=01011011
–X4=-1011011,[X4]1’s compl=10100100
•[+0]1’s compl=00000000;
[-0]1’s compl=11111111
Number System Range
Unsigned [0,2^N-1]
Sign/Magnitude [-(2(N-1)-1),2(N-1)-1]
One’s Complement [-(2(N-1)-1),2(N-1)-1]
Two’s Complement [-2(N-1),2(N-1)-1]
Overflow(溢出)
•Digital systems operate on a fixed number of bits
•Overflow: when result is too big to fit in the available number of bits
•See previous example of 11+6
Overflow Examples
Increasing Bit Width(扩展位数)
Extend number from N to M bits(M>N)
Zero-extension(零扩展)
•Zeros copied to msb’s
•Value changes for negative number
Sign-extension(符号扩展)
•Sign bit copied to msb’s
•Number value is same