Part II : Lecture III 240-334 By Wannarat

Multiplication 0010 (multiplicand) x 1011 (multiplier) ???? 240-334 By Wannarat

Unsign Combinational Multiplier 240-334 By Wannarat

Multiplication : First Version (Unsign) 240-334 By Wannarat

Multiplication : First Version (contd.) 240-334 By Wannarat

Analyze First Version 1 clock per cycle 50 % of bit in multiplicand always = 0 => 64-bit adder is wasted 0’s inserted in left of multiplicand as shifted => lead significant bits of product never changed once formed 240-334 By Wannarat

Multiplication : Second Version 240-334 By Wannarat

Multiplication : Second Version (Contd.) 240-334 By Wannarat

Analyze Second Version Product register wasted space that exactly matches size of multiplier Combine Multiplier register and Product register 240-334 By Wannarat

Multiplication : Third Version 240-334 By Wannarat

Multiplication : Third Version (Contd.) 240-334 By Wannarat

Analyze Third Version 2 steps per bit because multiplier & product combined MIPS registers Hi, Lo are left and right half of product 240-334 By Wannarat

Booth’s Algorithm 240-334 By Wannarat

Example : 2 x 7 240-334 By Wannarat

Example : 2 x -3 240-334 By Wannarat

Shifter : 2 kinds 240-334 By Wannarat

Part III : Lecture III 240-334 By Wannarat

Divide 240-334 By Wannarat

Divide : First Version 240-334 By Wannarat

Divide : First Version (Contd.) 240-334 By Wannarat

Analyze First Version 50% bits in divisor always 0 =>1/2 of 64-bit adder is wasted => 1/2 divisor is wasted 1 step cannot produce a 1 in quotient bit => Switch order to shift first 240-334 By Wannarat

Divide : Second Version 240-334 By Wannarat

Divide : Second Version (Contd.) 240-334 By Wannarat

Analyze Second Version Eliminate Quotient register by combining with Remainder as shifted left 240-334 By Wannarat

Divide : Third Version 240-334 By Wannarat

Divide : Third Version (Contd.) 240-334 By Wannarat

Analyze Third Version Do Analyze by yourself 240-334 By Wannarat

Floating Point : IEEE754 240-334 By Wannarat

Floating-point Representation -0.75 = -3/4 = -3/22 = -11/ 22 = -0.11 = -1.1x 2-1 = (-1)s x (1 + signifiand) x 2 (exponent-127) = (-1) x (1+.1000 0000) x 2(126-127) 1 01111110 1000 0000 0000 0000 0000 000 S E M 1-bit 8-bit 23-bit 240-334 By Wannarat

Floating-point Addition 9.999 x 101 + 1.610x10-1 Step1 : Change exponent as : 1.610 x 10 -1 = 0.016 x 101 Step2 : Add significands 9.999 (10) + 0.016 (10) 10.015 (10) Sum = 10.015 x 101 240-334 By Wannarat

Floating-point Addition 9.999 x 101 + 1.610x10-1 Step3 : correct it (normalization) : 10.015 x 10 1 = 1.0015 x 102 Step4 : Four digits for significand 1.002 x 102 240-334 By Wannarat

Example Floating-point Addition 0.5 + (-0.4375) 0.5 = 1/2 = 1/21 = 0.1 x 20 = 1.00 x 2-1 -0.4375 = -7/16 = -7/24 = - 0.0111 = -1.110 x 2-2 step 1 : -0.111 x 2-1 step 2 : 1.0x 2-1 + (-0.111 x 2-1)=0.001 x 2-1 step 3 : 1.0 x 2 -4 step 4 : 0.0625 240-334 By Wannarat

Multiplication Floating-point Study in Text Book by yourself. 240-334 By Wannarat

Next on Lecture 4 240-334 By Wannarat