EJERCICIOS DE SISTEMA DE NUMERACION

1. DIVISIONES
SUCESIVAS
1. 495 7
5 70 7
0 10 7
3 1
495 = 1305(7)
1 * 73 + 3 * 72 + 0 * 71 + 5 * 70
343 + 147 + 0 + 5
495
2.
1 * 83 + 7 * 82 + 5 * 81 + 1 * 80
512 + 448 + 40 + 1
1001
3.
7 * 94 + 5 * 93 + 7 * 92 + 0 * 91 + 4 * 90
45927 + 3645 + 567 + 0 + 4
50143
1001 8
1 125 8
5 15 8
7 1
1001= 1751(8)
50143 9
4 5571 9
0 619 9
7 68 9
5 7
50143= 75704(9)

2. 4. 343478 5
3 68695 5
0 13739 5
4 2747 5
2 549 5
4 109 5
4 21 5
1 4
343478 = 41442403(5)
4 * 57 + 1 * 56 + 4 * 55 + 4 * 54 + 2 * 53 + 4 * 52 + 0 * 51 + 3 * 50
312500 + 15625 + 12500 + 100 + 2500 + 250 + 3
343478

3. DESCOMPOSICIÓN POLINÓMICA
1. 5X4YZ( 7)
5 * 74 + X * 73 + 4 * 72 + Y * 71 + Z * 70
12005 + 343X + 196 + 7Y +Z
12201 + 343X + 7Y + Z
2. 4653(mn)
4 * mn3 + 6 * mn2 + 5 * mn1 + 3 * mn0
4mn3 + 6mn2 + 5mn + 3
mn (4mn2 + 6mm + 5) +3
3. X4 + Y3 + Z2
(c)
X4 * c2 + Y3 * c1 + Z2 * C0
X4c2 + Y3c1 + Z2
C (X4c1 + Y3) + Z2
4. 5abcd(XY)
5 * xy4 + a * xy3 + b * xy2 + c * xy1 + d * xy0
5xy4 + axy3 + bxy2 + cxy1 + d
xy (5xy3 + axy2 + bxy + c) + d
5. Abcde(a
3
b
2
)... LA “A Y B ” MAYUSCALAS TIENEN EL VALOR SIGUIENTE A=10 ; B= 11
10 * (a3b2)4 + b *(a3b2 )3 + c * (a3b2)2 + d * (a3b2)1 + e * (a3b2)0
(10a3b2)4 + (ba3b2 )3 + (ca3b2)2 + (da3b2)1 + e
(a3b2)1[10(a3b2)3+ (ba3b2 )3 + (ca3b2) + d]+ e