Binary, Hex and ASCII: A Practical Student Guide

Worked place-value check

1. Build 93 from place values

Decimal uses powers of ten; binary uses powers of two. An eight-bit row has place values 128, 64, 32, 16, 8, 4, 2, 1 from left to right. Each bit tells you whether to include that value.

For 93, choose 64, then 16, then 8, then 4, then 1: 93 = 64 + 16 + 8 + 4 + 1. Put 1 in those positions and 0 elsewhere. The result is 01011101 in an eight-bit display. Check it by adding the selected place values back together.

A leading zero adds no value: 1011101 and 01011101 both represent 93 as unsigned binary. The leading zero is useful when you want to display a complete byte (eight bits). The Number Converter pads to whole bytes, up to 32 bits; it does not silently discard large values.

2. Read hex four bits at a time

Hexadecimal has sixteen digit values: 0–9, then A=10, B=11, C=12, D=13, E=14 and F=15. Four binary bits make one hex digit. Split 01011101 into 0101 and 1101: those groups are 5 and D, so the hex result is 5D.

Check in decimal: 5 × 16 + 13 = 93. Two hex digits display one byte. Prefixes such as 0b01011101 and 0x5D identify the base; they are not extra digits. The quick Number Converter accepts decimal only. For binary or hex operands, select that input base in Binary Calculator.

3. ASCII is a character code

In standard ASCII, decimal 93 is the closing square bracket ]. This does not mean that the text 93 is one bracket: the two text characters 9 and 3 have separate ASCII codes 57 and 51. Decide whether you are converting a numeric code or encoding a string.

Standard ASCII covers 0–127. The chart displays each code as an eight-bit byte with a leading zero. Codes 0–31 and 127 are controls, such as LF for line feed and DEL for delete; 32 is a space. The tool labels these instead of inserting invisible control characters. Values above 127 have no standard ASCII character. Unicode and UTF-8 are broader topics, not an extended ASCII assumption.

4. The same bits can have a different meaning

An unsigned eight-bit integer ranges from 0 to 255. Eight-bit two's complement ranges from −128 to 127. For N bits, the unsigned range is 0 through 2^N−1, and the signed range is −2^(N−1) through 2^(N−1)−1.

The bits 11111111 mean 255 unsigned or −1 signed. For a negative two's-complement pattern, you can subtract 2^N from its unsigned value: 255−256 = −1. To form −5 in eight bits, start with 00000101, invert the bits to 11111010, then add 1 to get 11111011.

Changing signed mode in Binary Calculator preserves the bits and explains their new interpretation. Changing width preserves the integer when it fits: signed −5 widens to 1111111111111011 at sixteen bits. A narrowing that cannot preserve the value is rejected. A base change keeps the same bits.

5. Separate the exact answer from stored bits

With eight-bit unsigned storage, 255+1 has exact answer 256 but stored answer 00000000. The carry exceeds the width, so the result wraps and the tool reports overflow. In eight-bit signed mode, 127+1 has exact answer 128 but stored interpretation −128, also overflow.

A right shift discards low bits. Unsigned right shift fills the left side with zeros; signed right shift repeats the sign bit. Left shift discards high bits and reports them separately. Bitwise AND, OR and XOR compare corresponding bits; Boolean + in Truth Tables means OR, while + in Binary Calculator means arithmetic addition.

Try it in the tool

Open Logic Tools and choose Number Converter. Enter 93 and press Convert number or Enter. Expect binary 01011101, hex 5D and ASCII ]. Expand Standard ASCII chart to compare nearby codes.

Next choose Binary Calculator. Select binary input, eight bits and unsigned mode; enter 11111111 as the first operand and 0 as the second, then Calculate. Switch to signed mode and calculate again. The bits stay the same while the decimal interpretation changes from 255 to −1.