Let’s convert each binary number to decimal (denary) step by step.
Binary numbers are made of 0s and 1s. Each digit represents a power of 2, starting from the rightmost digit (which is 2⁰ = 1), then moving left: 2¹ = 2, 2² = 4, 2³ = 8, and so on.
To convert, we add up the values where there’s a “1” in that position.
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Example for understanding:
Take binary `101` →
Right to left:
- Position 0 (right): 1 → 2⁰ = 1
- Position 1: 0 → skip
- Position 2 (left): 1 → 2² = 4
Total = 4 + 1 =
5
Now let’s do all 24 problems carefully.
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Column 1:
1)
11010101
Positions (from right, starting at 0):
Bit positions with 1: 7,6,4,2,0
→ 2⁷=128, 2⁶=64, 2⁴=16, 2²=4, 2⁰=1
Sum: 128+64=192; 192+16=208; 208+4=212; 212+1=
213
2)
10100000
Bits set: 7,5 → 128 + 32 =
160
3)
11000111
Bits: 7,6,2,1,0 → 128+64=192; +4=196; +2=198; +1=
199
4)
10100111
Bits: 7,5,2,1,0 → 128+32=160; +4=164; +2=166; +1=
167
5)
11011111
Bits: 7,6,4,3,2,1,0 → 128+64=192; +16=208; +8=216; +4=220; +2=222; +1=
223
6)
10111101
Bits: 7,5,4,3,2,0 → 128+32=160; +16=176; +8=184; +4=188; +1=
189
7)
01110000
Bits: 6,5,4 → 64+32=96; +16=
112
8)
10001110
Bits: 7,3,2,1 → 128 + 8=136; +4=140; +2=
142
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Column 2:
9)
01101110
Bits: 6,5,3,2,1 → 64+32=96; +8=104; +4=108; +2=
110
10)
11110000
Bits: 7,6,5,4 → 128+64=192; +32=224; +16=
240
11)
11001000
Bits: 7,6,3 → 128+64=192; +8=
200
12)
10000011
Bits: 7,1,0 → 128 + 2 + 1 =
131
13)
00000001
Only bit 0 →
1
14)
10000010
Bits: 7,1 → 128 + 2 =
130
15)
11101110
Bits: 7,6,5,3,2,1 → 128+64=192; +32=224; +8=232; +4=236; +2=
238
16)
10101010
Bits: 7,5,3,1 → 128+32=160; +8=168; +2=
170
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Column 3:
17)
01100011
Bits: 6,5,1,0 → 64+32=96; +2=98; +1=
99
18)
00011100
Bits: 4,3,2 → 16+8=24; +4=
28
19)
00110001
Bits: 5,4,0 → 32+16=48; +1=
49
20)
11100011
Bits: 7,6,5,1,0 → 128+64=192; +32=224; +2=226; +1=
227
21)
11011000
Bits: 7,6,4,3 → 128+64=192; +16=208; +8=
216
22)
10010000
Bits: 7,4 → 128 + 16 =
144
23)
01010100
Bits: 6,4,2 → 64+16=80; +4=
84
24)
11101011
Bits: 7,6,5,3,1,0 → 128+64=192; +32=224; +8=232; +2=234; +1=
235
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Final Answer:
1) 213
2) 160
3) 199
4) 167
5) 223
6) 189
7) 112
8) 142
9) 110
10) 240
11) 200
12) 131
13) 1
14) 130
15) 238
16) 170
17) 99
18) 28
19) 49
20) 227
21) 216
22) 144
23) 84
24) 235
Parent Tip: Review the logic above to help your child master the concept of binary to decimal worksheet.
