Convert decimal 102 to its 8-bit 2's complement binary representation:
76543210 01100110 102 51 50 25 24 12 6 3 1 102=a7*2^7 + a6*2^6 + a5*2^5 + a4*2^4 + a3*2^3 + a2*2^2 + a1*2^1 + a0*2^0 Because 102 is positive number, a7=0. Because 102 is even number, a0=0. 102= a6*2^6 + a5*2^5 + a4*2^4 + a3*2^3 + a2*2^2 + a1*2^1 A. Since 102 is even, we can divide both sides by 2: 51= a6*2^5 + a5*2^4 + a4*2^3 + a3*2^2 + a2*2^1 + a1*2^0 Because 51 is odd, a1=1. B. Decrement by 1 both sides: 50= a6*2^5 + a5*2^4 + a4*2^3 + a3*2^2 + a2*2^1 C. Since 50 is even, divide both sides by 2: 25= a6*2^4 + a5*2^3 + a4*2^2 + a3*2^1 + a2*2^0 D. Since 25 is odd, therefore a2=1 E. Subtract 1 and divide by 2: 24= a6*2^4 + a5*2^3 + a4*2^2 + a3*2^1 12= a6*2^3 + a5*2^2 + a4*2^1 + a3*2^0 F. Since 12 is even, therefore a3=0 12= a6*2^3 + a5*2^2 + a4*2^1 6= a6*2^2 + a5*2^1 + a4*2^0 F. Since 6 is even, therefore a4=0 Divide by 2: 3= a6*2^1 + a5*2^0 G. Since 3 is odd, therefore a5=1 Subtract 1 and divide by 2: 2= a6*2^1 1= a6*2^0 H. Since 1 is odd, therefore a6=1