COMPENG 2DI4 Lecture : NUMBER SYSTEMS AND CONVERSION

• School: McMaster University
• Department: Computer Engineering
• Course: COMPENG 2DI4
• Professor: Xudong Zhu

Document Summary

Click the mouse to move to the next page. Use the esc key to exit this chapter. Base r has digits 0, 1, 2, , r-1. Base 4 uses digits 0, 1, 2, 3. Base 8 (octal) uses digits 0, 1, 2, 3, 4, 5, 6, 7. Base 10 (decimal) uses digits 0, 1, 2, 3, 4, 5, 6, 7, 8, Base 16 (hexadecimal) uses digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a (=10), b(=11), c(=12), d(=13), e(=14), Convert number 23 to binary: 11201, 10001, 10111, 11101, 11111. N = (anan-1an-2 a2a1a0)r = anrn + an-1rn-1 + a2r2+a1r1+a0. N/r = anrn-1 + an-1rn-2 + a2r1+a1=q1 remainder a0. Q1/r = anrn-2 + an-1rn-3 + a2=q2 remainder a1. Q2/r = anrn-3 + an-1rn-4 + a3=q3 remainder a2. By successive divisions we recovered a0, a1, a2, Convert number . 65 to binary a) b) c) d) e) F = (. a-1a-2a-3 a-m)r = a-1r-1 + a-2r-2 + a- mr-m.