Step $1$: Initialize the product register with $0$s and create an extra bit to handle the sign bit extension.

Product Register $($PR$)=0000000$

Step$2$:$$Extend$$the$$sign$$bit$$of$$A$$and$$B$$for$$the$$algorithm$$

Extended A $=0010111$

Extended B $=1110110$

Step $3$: Start the Booth's algorithm by examining adjacent pairs of bits in the multiplier B$.$

Using the Booth's algorithm, perform the following steps:

WhenB$[$i:i$+1]=10,$ add A to PR$.$

WhenB$[$i:i$+1]=01,$ subtract A from PR$.$

Iteration $1$: B$[5$:$4]=10,$ so add A to PR:PR$=0000000+10,111=10,111($shift right A and PR$)$

Iteration $2$: B$[4$:$3]=11,$ no operation needed as this pair doesn't match $10$ or $01$: PR $=0001011($shift right A and PR$)$

Iteration $3$: B$[3$:$2]=11,$ no operation needed: PR $=0000101($shift right A and PR$)$

Iteration $4$: B$[2$:$1]=01,$ so subtract A from PR: PR $=1111010+0010111=0000001($shift right A and PR$)$

Iteration $5$: B$[1$:$0]=10,$ so add A to PR: PR $=0000001+0010111=0011000($shift right A and PR$)$

Iteration $6$: B$[0]=0($ignore as single bit$),$ no operation needed: PR $=0001100($shift right A and PR$)$