Number Base Conversion Practice Problems — Binary, Decimal, Hex

The fastest way to master base conversions is practice. 30 problems with answers. Work by hand, check with the Number Base Converter.

Level 1: Binary and Decimal

Decimal to binary: (1) 7 (2) 15 (3) 25 (4) 42 (5) 100

Binary to decimal: (6) 1011 (7) 11001 (8) 101010 (9) 11111111 (10) 10000000

Answers

#	Problem	Answer	Method
1	7→bin	111	4+2+1
2	15→bin	1111	8+4+2+1
3	25→bin	11001	16+8+1
4	42→bin	101010	32+8+2
5	100→bin	1100100	64+32+4
6	1011→dec	11	8+2+1
7	11001→dec	25	16+8+1
8	101010→dec	42	32+8+2
9	11111111→dec	255	All 8 bits
10	10000000→dec	128	Only bit 7

Level 2: Hexadecimal

Decimal to hex: (11) 26 (12) 127 (13) 255 (14) 1000 (15) 48879

Hex to decimal: (16) 1A (17) 7F (18) FF (19) 3E8 (20) BEEF

Answers

#	Problem	Answer	Method
11	26→hex	1A	26/16=1r10(A)
12	127→hex	7F	127/16=7r15(F)
13	255→hex	FF	255/16=15r15
14	1000→hex	3E8	1000/16=62r8, 62/16=3r14(E)
15	48879→hex	BEEF
16	1A→dec	26	1×16+10
17	7F→dec	127	7×16+15
18	FF→dec	255	15×16+15
19	3E8→dec	1000	3×256+14×16+8
20	BEEF→dec	48879	11×4096+14×256+14×16+15

Level 3: Binary to Hex Grouping

(21) 10110011 (22) 11111110 (23) 101011001101 (24) A5→bin (25) DEAD→bin

Answers

#	Problem	Answer	Method
21	10110011→hex	B3	1011=B, 0011=3
22	11111110→hex	FE	1111=F, 1110=E
23	101011001101→hex	ACD	1010=A, 1100=C, 1101=D
24	A5→bin	10100101	A=1010, 5=0101
25	DEAD→bin	1101111010101101	D=1101,E=1110,A=1010,D=1101

Level 4: Octal and Mixed

(26) 493→oct (27) Oct 755→dec (28) Oct 644→bin (29) 110100101→oct (30) FF→oct

Answers

#	Problem	Answer	Method
26	493→oct	755	493/8=61r5,61/8=7r5,7/8=0r7
27	Oct 755→dec	493	7×64+5×8+5
28	Oct 644→bin	110100100	6=110,4=100,4=100
29	110100101→oct	645	110=6,100=4,101=5
30	FF→oct	377	FF=255, div by 8

Speed Tips

• Memorize powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256
• Memorize hex nibbles: A=10, B=11, C=12, D=13, E=14, F=15
• Binary↔hex: always 4-bit grouping, never division
• Verify by converting back to original base
• Converter checks answers instantly

More: Base64 Encoder, Regex Tester.