Page 273 - FUNDAMENTALS OF COMPUTER

NPP Number System, Boolean Algebra and Logic Circuits 273

Quotient = 000 ^mJ\$c = 000

Step 1 ⇒ 1011 – 0100 = + 0111

Quotient = 001 ^mJ\$c = 001
Step 2 ⇒ 0111 – 0100 = + 0011
Quotient = 010 ^mJ\$c = 010

Step 3 ⇒ 0011 – 0100 = – Ve Result

Remainder = 0011 eof\$c = 0011
Therefore the last positive difference AV: A§Va YZmË_H$ A§Va (0011) eof\$c h¡ VWm
(0011) is Remainder and (010) is the quo-
tient. The quotient represents number of 010 ^mJ\$c h¢, ^mJ\$c Xem©Vm h¡ {H$ {H$VZr ~ma
times positive difference is obtained. The YZmË_H$ A§Va àmßV hþAmŸ& AJa KQ>mVo g_` A§V _|
indication of negative difference will be CYma H$s Amdí`H$Vm hmoVr h¡ Vmo `h Xem©Vm h¡ {H$
the need of borrow at the end of subtrac-
tion. NPP F$UmË_H$ n[aUm_ h¢Ÿ&
3.31 Binary Division (Restoring Method 3.31 ~mBZar {d^mOZ (arñQ>mo[a¨J _oWS> `m
or Long-hand Method) bm°ÝJ-hoÝS> _oWS>)

In this method of Binary Division start from Bg {d{Y _| ^mÁ` H$s MSB go àma§^ H$aVo h¢ŸAm¡a
MSB of the dividend and see if it is divisible by XoIVo h¡ {H$ Bg_| ^mOH$ H$m ^mJ OmEJm AWdm ZhtŸ&
divisor. If it is divisible, the bit in the Quotient `{X ^mJ OmVm h¡ Vmo ^mJ\$b _| {~Q> H$mo 1 {bIVo h¢
is set to ‘1’ else it is set to ‘0’. If there is a borrow AÝ`Wm 0 {bIVo h¢Ÿ& `{X ^mJ Zhr OmVm h¡ Vmo KQ>mVo
at the end of subtraction it shows that the quo- g_` A§V _| CYma H$s Amdí`H$Vm hmoVr h¡Ÿ& Bg pñW{V
tient bit is zero and we have to restore the bit _| h_| ^mOH$ H$mo nwZ… Omo‹S>H$a dhr {~Q> nwZ… àmá H$aZr
by adding the divisor. Now append the next bit hmoVr h¡Ÿ& `{X ^mJ Mbm OmVm h¡ Vmo AJbr {~Q> H$mo CVma
of the dividend. After appending the LSB and boVo h¢Ÿ& Eogm H$aVo-H$aVo A§V _| LSB H$mo CVmaZo na
{d{Y H$m A§V hmo OmVm h¡Ÿ& `{X A§V _| CVmar JB© {~Q>
subtracting the divisor stop the procedure. The Ho$ níMmV² ^mJ Zht OmVm h¡ Vmo `h eof\$b hmoVm h¡Ÿ&
following example illustrates the procedure: AmJo {X`o J`o CXmhaU H$mo Ü`mZ go XoIZo na CnamoŠV {d{Y
We have to divide 1001 by 10 : ñnï> hmoVr h¡ … h‘| 1001 H$mo 10 go ^mJ XoZm h¡&